<<<<<<< HEAD glinski_metabolites

tested hypotheses

things to do

install and load supporting libraries

##          nodename 
## "DZ2626UTPURUCKE"
## [1] "R version 3.2.3 (2015-12-10)"
## 
## Attaching package: 'MASS'
## 
## The following object is masked from 'package:dplyr':
## 
##     select
## 
## 
## 'drc' has been loaded.
## 
## Please cite R and 'drc' if used for a publication,
## for references type 'citation()' and 'citation('drc')'.
## [1] "list of loaded packages: "
##  [1] "scatterplot3d" "ggplot2"       "drc"           "MASS"         
##  [5] "xtable"        "zoo"           "knitr"         "dplyr"        
##  [9] "rmarkdown"     "stats"         "graphics"      "grDevices"    
## [13] "utils"         "datasets"      "methods"       "base"

import experimental exposure and microsomal data

Load csv files with experimental data and microsome data sets. The beolw may return false but still be OK if rstudio does not have privileges to data directory (e.g., attached drive).

## [1] "Root directory location: k:/git/glinski_metabolites/"
## [1] "check to see if R can access files OK: FALSE"
## [1] "outliers:"
##     time   parent  analyte     matrix     conc replicate microMexp
## 96    30 atrazine atrazine microsomes 158.6508         1       125
## 99    60 atrazine atrazine microsomes 170.6522         1       125
## 125    0 atrazine atrazine microsomes 152.8226         1       200
## 126    0 atrazine atrazine microsomes 135.8870         2       200
## 127    0 atrazine atrazine microsomes 146.1521         3       200
## 128   15 atrazine atrazine microsomes 200.8988         1       200
## 129   15 atrazine atrazine microsomes 134.8156         2       200
## 130   15 atrazine atrazine microsomes 211.5786         3       200
## 131   30 atrazine atrazine microsomes 193.1223         1       200
## 132   30 atrazine atrazine microsomes 210.4726         2       200
## 133   30 atrazine atrazine microsomes 213.5141         3       200
## 134   60 atrazine atrazine microsomes 197.4426         1       200
## 135   60 atrazine atrazine microsomes 146.8087         2       200
## 136   60 atrazine atrazine microsomes 201.9011         3       200
## 137   90 atrazine atrazine microsomes 127.9031         1       200
## 138   90 atrazine atrazine microsomes 203.6292         2       200
## 139   90 atrazine atrazine microsomes 128.0068         3       200

experimental exposure data structure

Check out structure of imported data sets.

str(micro)
## 'data.frame':    352 obs. of  6 variables:
##  $ time     : int  2 2 2 2 4 4 4 4 12 12 ...
##  $ parent   : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte  : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix   : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 1 1 1 1 1 ...
##  $ conc     : num  3.07 3.69 4.7 1.89 7.62 ...
##  $ replicate: int  1 2 3 4 1 2 3 4 1 2 ...

Set time and replicate fields as factors for later statistical inference.

microsome experiment data structure

Check out structure of imported data set for the microsome analysis.

str(microsome)
## 'data.frame':    1106 obs. of  7 variables:
##  $ time     : int  0 0 0 15 15 15 30 30 30 60 ...
##  $ parent   : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte  : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix   : Factor w/ 1 level "microsomes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ conc     : num  1.208 1.596 1.362 0.551 1.347 ...
##  $ replicate: int  1 2 3 1 2 3 1 2 3 1 ...
##  $ microMexp: num  0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 ...

Set time and replicate fields as factors for later statistical inference.

## 'data.frame':    1106 obs. of  7 variables:
##  $ time     : int  0 0 0 15 15 15 30 30 30 60 ...
##  $ parent   : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte  : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix   : Factor w/ 1 level "microsomes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ conc     : num  1.208 1.596 1.362 0.551 1.347 ...
##  $ replicate: Factor w/ 4 levels "1","2","3","4": 1 2 3 1 2 3 1 2 3 1 ...
##  $ microMexp: num  0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 ...

analyze microsomal data

The microsomal experiment has 3-4 replicates for each pesticide. The experiment progressively increases the concentration of the substrate (microMexp) and measures the enzyme velocity. At each substrate concentration the reaction is quenched after a specific period of time (0, 15, 30, 60, 90 mins). This time series data is used to estimate a slope associated with each substrate concentration. Substrate concentration and linear velocity slopes are then fit using Michaelis-Menten kinetics to estimate reaction rates for each pesticide.

atrazine

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  0.712"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 1.208049891" "Concs = 1.59580743"  "Concs = 1.362262655"
##  [4] "Concs = 0.551435364" "Concs = 1.346911275" "Concs = 1.212444791"
##  [7] "Concs = 1.13491833"  "Concs = 1.082466929" "Concs = 1.113889522"
## [10] "Concs = 0.918015161" "Concs = 0.819916078" "Concs = 0.830401682"
## [13] "Concs = 0.60193292"  "Concs = 0.514615471" "Concs = 0.543046503"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    1.309205    -0.008208  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.63464 -0.01209  0.02637  0.06251  0.28660 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.309205   0.083093  15.756 7.52e-10 ***
## Time[ind]   -0.008208   0.001641  -5.003 0.000242 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2053 on 13 degrees of freedom
## Multiple R-squared:  0.6582, Adjusted R-squared:  0.6319 
## F-statistic: 25.03 on 1 and 13 DF,  p-value: 0.0002416

##  (Intercept)    Time[ind] 
##  1.309205033 -0.008208481 
##                   2.5 %       97.5 %
## (Intercept)  1.12969277  1.488717294
## Time[ind]   -0.01175294 -0.004664018
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
##  [1] "Concs = 8.602230146" "Concs = 8.531210299" "Concs = 8.218650517"
##  [4] "Concs = 8.453642708" "Concs = 7.964608184" "Concs = 7.94451139" 
##  [7] "Concs = 7.680602046" "Concs = 7.527336918" "Concs = 7.478498249"
## [10] "Concs = 5.659397741" "Concs = 6.36413415"  "Concs = 6.660240451"
## [13] "Concs = 6.34249619"  "Concs = 5.477249479" "Concs = 5.670032215"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      8.5223      -0.0347  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.78076 -0.06665  0.00889  0.13964  0.45186 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  8.522319   0.119538   71.29  < 2e-16 ***
## Time[ind]   -0.034703   0.002512  -13.82 3.79e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2912 on 13 degrees of freedom
## Multiple R-squared:  0.9362, Adjusted R-squared:  0.9313 
## F-statistic: 190.9 on 1 and 13 DF,  p-value: 3.789e-09

## (Intercept)   Time[ind] 
##  8.52231931 -0.03470261 
##                   2.5 %      97.5 %
## (Intercept)  8.26407296  8.78056567
## Time[ind]   -0.04012886 -0.02927636
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  3.1684"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 3.365067675" "Concs = 3.642810527" "Concs = 3.434256239"
##  [4] "Concs = 3.840288882" "Concs = 3.471244145" "Concs = 4.21892194" 
##  [7] "Concs = 3.04149649"  "Concs = 3.107056916" "Concs = 2.539792287"
## [10] "Concs = 2.350740689" "Concs = 2.184285874" "Concs = 1.868856626"
## [13] "Concs = 1.487945081" "Concs = 1.746448606" "Concs = 1.279189407"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     3.76182     -0.02538  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.46055 -0.26287  0.01058  0.10930  0.83784 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.761823   0.145888  25.786 1.51e-12 ***
## Time[ind]   -0.025383   0.002881  -8.812 7.64e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3605 on 13 degrees of freedom
## Multiple R-squared:  0.8566, Adjusted R-squared:  0.8456 
## F-statistic: 77.65 on 1 and 13 DF,  p-value: 7.644e-07

## (Intercept)   Time[ind] 
##  3.76182347 -0.02538282 
##                   2.5 %      97.5 %
## (Intercept)  3.44665102  4.07699592
## Time[ind]   -0.03160589 -0.01915975
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59" "Indices =  60"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 32.61853939" "Concs = 28.61877014" "Concs = 24.9941227" 
##  [4] "Concs = 30.1352595"  "Concs = 28.31360828" "Concs = 26.0438183" 
##  [7] "Concs = 30.34766105" "Concs = 27.74701672" "Concs = 25.6412683" 
## [10] "Concs = 28.51624079" "Concs = 26.35221344" "Concs = 24.78295594"
## [13] "Concs = 26.56519331" "Concs = 24.44743091" "Concs = 24.01565934"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    28.88318     -0.04121  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8891 -1.3931 -0.0584  1.6306  3.7354 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 28.88318    0.86801  33.275 5.74e-14 ***
## Time[ind]   -0.04121    0.01714  -2.404   0.0318 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.145 on 13 degrees of freedom
## Multiple R-squared:  0.3078, Adjusted R-squared:  0.2546 
## F-statistic: 5.782 on 1 and 13 DF,  p-value: 0.03182

## (Intercept)   Time[ind] 
##  28.8831817  -0.0412102 
##                   2.5 %       97.5 %
## (Intercept) 27.00795252 30.758410981
## Time[ind]   -0.07823653 -0.004183871
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  61" "Indices =  62" "Indices =  63" "Indices =  64"
##  [5] "Indices =  65" "Indices =  66" "Indices =  67" "Indices =  68"
##  [9] "Indices =  69" "Indices =  70" "Indices =  71" "Indices =  72"
## [13] "Indices =  73" "Indices =  74" "Indices =  75"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 31.69355406" "Concs = 32.50417088" "Concs = 39.73678741"
##  [4] "Concs = 29.59548976" "Concs = 36.16487256" "Concs = 37.40302159"
##  [7] "Concs = 27.6465584"  "Concs = 28.94210726" "Concs = 34.71955504"
## [10] "Concs = 31.19094038" "Concs = 35.96712185" "Concs = 33.12001232"
## [13] "Concs = 31.51869676" "Concs = 32.99095623" "Concs = 22.85692843"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    34.36984     -0.05042  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -6.975 -3.296  1.687  2.855  5.367 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 34.36984    1.62052  21.209 1.81e-11 ***
## Time[ind]   -0.05042    0.03200  -1.576    0.139    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.004 on 13 degrees of freedom
## Multiple R-squared:  0.1604, Adjusted R-squared:  0.0958 
## F-statistic: 2.483 on 1 and 13 DF,  p-value: 0.1391

## (Intercept)   Time[ind] 
## 34.36983650 -0.05042184 
##                  2.5 %      97.5 %
## (Intercept) 30.8689187 37.87075426
## Time[ind]   -0.1195473  0.01870365
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  76" "Indices =  77" "Indices =  78" "Indices =  79"
##  [5] "Indices =  80" "Indices =  81" "Indices =  82" "Indices =  83"
##  [9] "Indices =  84" "Indices =  85" "Indices =  86" "Indices =  87"
## [13] "Indices =  88" "Indices =  89" "Indices =  90"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 76.46874561" "Concs = 67.44424419" "Concs = 60.20571288"
##  [4] "Concs = 73.12305661" "Concs = 62.97208244" "Concs = 58.17491784"
##  [7] "Concs = 70.9357471"  "Concs = 60.89975615" "Concs = 54.39425099"
## [10] "Concs = 67.30936536" "Concs = 56.7524779"  "Concs = 50.73568923"
## [13] "Concs = 64.11432499" "Concs = 53.06960934" "Concs = 51.00465026"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      66.948       -0.131  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -8.625 -5.449 -2.092  8.028  9.521 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 66.94770    2.83785  23.591 4.69e-12 ***
## Time[ind]   -0.13096    0.05603  -2.337   0.0361 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.012 on 13 degrees of freedom
## Multiple R-squared:  0.2959, Adjusted R-squared:  0.2417 
## F-statistic: 5.462 on 1 and 13 DF,  p-value: 0.03608

## (Intercept)   Time[ind] 
##  66.9476963  -0.1309587 
##                 2.5 %       97.5 %
## (Intercept) 60.816898 73.078494940
## Time[ind]   -0.252011 -0.009906267
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  91"  "Indices =  92"  "Indices =  93"  "Indices =  94" 
##  [5] "Indices =  95"  "Indices =  96"  "Indices =  97"  "Indices =  98" 
##  [9] "Indices =  99"  "Indices =  100" "Indices =  101" "Indices =  102"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 15"
##  [6] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 90"
## [11] "Times = 90" "Times = 90"
##  [1] "Concs = 88.09234635" "Concs = 85.70476499" "Concs = 107.9737675"
##  [4] "Concs = 85.24148342" "Concs = 85.54901737" "Concs = 83.6386001" 
##  [7] "Concs = 83.07467838" "Concs = 78.21161933" "Concs = 84.54185693"
## [10] "Concs = 80.88478508" "Concs = 79.00424811" "Concs = 78.20108166"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     90.1940      -0.1257  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.4892 -3.1378 -2.4307  0.5629 19.6649 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  90.1940     3.1499  28.634 6.28e-11 ***
## Time[ind]    -0.1257     0.0592  -2.123   0.0597 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.892 on 10 degrees of freedom
## Multiple R-squared:  0.3107, Adjusted R-squared:  0.2418 
## F-statistic: 4.507 on 1 and 10 DF,  p-value: 0.05972

## (Intercept)   Time[ind] 
##  90.1939928  -0.1256761 
##                  2.5 %       97.5 %
## (Intercept) 83.1756334 97.212352214
## Time[ind]   -0.2575766  0.006224427
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  103" "Indices =  104" "Indices =  105" "Indices =  106"
##  [5] "Indices =  107" "Indices =  108" "Indices =  109" "Indices =  110"
##  [9] "Indices =  111" "Indices =  112" "Indices =  113" "Indices =  114"
## [13] "Indices =  115" "Indices =  116" "Indices =  117" "Indices =  118"
## [17] "Indices =  119" "Indices =  120" "Indices =  121" "Indices =  122"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15"
##  [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 60" "Times = 90" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 111.7791798" "Concs = 108.954701"  "Concs = 113.7158271"
##  [4] "Concs = 107.5512697" "Concs = 110.8050341" "Concs = 114.7205562"
##  [7] "Concs = 107.1291095" "Concs = 110.2111065" "Concs = 106.4113993"
## [10] "Concs = 109.2588435" "Concs = 108.8110859" "Concs = 98.45121644"
## [13] "Concs = 105.7397626" "Concs = 103.5578664" "Concs = 109.569591" 
## [16] "Concs = 103.2077499" "Concs = 96.26533592" "Concs = 104.9741825"
## [19] "Concs = 105.7942757" "Concs = 95.31462118"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    110.8882      -0.1097  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.1469 -1.9786  0.9295  1.9524  5.4774 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 110.88819    1.37221  80.810  < 2e-16 ***
## Time[ind]    -0.10967    0.02709  -4.048 0.000755 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.915 on 18 degrees of freedom
## Multiple R-squared:  0.4765, Adjusted R-squared:  0.4474 
## F-statistic: 16.38 on 1 and 18 DF,  p-value: 0.0007553

## (Intercept)   Time[ind] 
##  110.888186   -0.109668 
##                   2.5 %       97.5 %
## (Intercept) 108.0052898 113.77108184
## Time[ind]    -0.1665906  -0.05274528
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  123" "Indices =  124" "Indices =  125" "Indices =  126"
##  [5] "Indices =  127" "Indices =  128" "Indices =  129" "Indices =  130"
##  [9] "Indices =  131" "Indices =  132" "Indices =  133" "Indices =  134"
## [13] "Indices =  135" "Indices =  136" "Indices =  137"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 31" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 135.98518"   "Concs = 118.5627805" "Concs = 138.8461629"
##  [4] "Concs = 111.0650322" "Concs = 110.394181"  "Concs = 107.7699691"
##  [7] "Concs = 110.0390245" "Concs = 133.1636589" "Concs = 106.6453068"
## [10] "Concs = 125.4094086" "Concs = 132.3152295" "Concs = 129.5529012"
## [13] "Concs = 107.9475473" "Concs = 109.2892497" "Concs = 110.9269157"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##   122.96364     -0.09649  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -13.746 -10.241  -4.401  12.700  15.883 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 122.96364    4.82709  25.474 1.76e-12 ***
## Time[ind]    -0.09649    0.09524  -1.013    0.329    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.91 on 13 degrees of freedom
## Multiple R-squared:  0.07318,    Adjusted R-squared:  0.001888 
## F-statistic: 1.026 on 1 and 13 DF,  p-value: 0.3295

##  (Intercept)    Time[ind] 
## 122.96363586  -0.09648804 
##                   2.5 %      97.5 %
## (Intercept) 112.5353325 133.3919392
## Time[ind]    -0.3022315   0.1092554
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  0.712 10 3.168 50 75 ...
##  $ vel: num  41 174 127 206 252 ...
##        sub       vel
## 1   0.7120  41.04241
## 2  10.0000 173.51305
## 3   3.1684 126.91411
## 4  50.0000 206.05101
## 5  75.0000 252.10918
## 6 100.0000 654.79328
## 7 125.0000 628.38045
## 8 150.0000 548.33976
## 9 250.0000 482.44019

We are interested in the reaction rate, v, which is a function of available substrate (pesticide) and the presence of an enzyme. We get Vmax from the asymptote and K = 0.5*Vmax. Biochemical reactions with a single substrate are typically assumed to follow Michaelis-Menten kinetics even if they deviate from the basic model assumptions.

We are fitting the 2-parameter model.

Used to estimate slopes.

dea

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.105334715" "Concs = 0.177716074" "Concs = 0.215668236"
##  [7] "Concs = 0.273065521" "Concs = 0.362248011" "Concs = 0.403265809"
## [10] "Concs = 0.502168642" "Concs = 0.64289193"  "Concs = 0.720570734"
## [13] "Concs = 0.725802164" "Concs = 0.865500124" "Concs = 0.956691847"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.028620     0.009439  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.15230 -0.03367 -0.01260  0.04921  0.12563 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0286203  0.0312329   0.916    0.376    
## Time[ind]   0.0094387  0.0006167  15.305 1.08e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07717 on 13 degrees of freedom
## Multiple R-squared:  0.9474, Adjusted R-squared:  0.9434 
## F-statistic: 234.3 on 1 and 13 DF,  p-value: 1.076e-09

## (Intercept)   Time[ind] 
## 0.028620334 0.009438665 
##                    2.5 %     97.5 %
## (Intercept) -0.038854153 0.09609482
## Time[ind]    0.008106383 0.01077095
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.062527948" "Concs = 0.066722432" "Concs = 0.073739184"
##  [7] "Concs = 0.13417786"  "Concs = 0.142144514" "Concs = 0.153899766"
## [10] "Concs = 0.359398841" "Concs = 0.284549411" "Concs = 0.293488967"
## [13] "Concs = 0.291970799" "Concs = 0.378114427" "Concs = 0.405964967"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.004784     0.004640  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.044227 -0.008723 -0.004784  0.005104  0.076243 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.004784   0.010614   0.451     0.66    
## Time[ind]   0.004640   0.000223  20.804 2.31e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02585 on 13 degrees of freedom
## Multiple R-squared:  0.9708, Adjusted R-squared:  0.9686 
## F-statistic: 432.8 on 1 and 13 DF,  p-value: 2.309e-11

## (Intercept)   Time[ind] 
## 0.004784043 0.004639529 
##                    2.5 %      97.5 %
## (Intercept) -0.018145174 0.027713259
## Time[ind]    0.004157742 0.005121316
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.692469949" "Concs = 0.598237597" "Concs = 0.603481745"
##  [7] "Concs = 1.23886552"  "Concs = 1.156190328" "Concs = 1.011651128"
## [10] "Concs = 2.056702931" "Concs = 1.850305243" "Concs = 1.516060546"
## [13] "Concs = 2.637550555" "Concs = 2.271829323" "Concs = 2.15464298" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.19461      0.02542  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.32748 -0.19461  0.02762  0.14305  0.33708 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.194607   0.086818   2.242   0.0431 *  
## Time[ind]   0.025417   0.001714  14.827 1.59e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2145 on 13 degrees of freedom
## Multiple R-squared:  0.9442, Adjusted R-squared:  0.9399 
## F-statistic: 219.8 on 1 and 13 DF,  p-value: 1.593e-09

## (Intercept)   Time[ind] 
##   0.1946066   0.0254169 
##                   2.5 %     97.5 %
## (Intercept) 0.007046883 0.38216639
## Time[ind]   0.021713543 0.02912026
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59" "Indices =  60"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.126910879" "Concs = 0.194298986" "Concs = 0.205689666"
##  [7] "Concs = 0.343048244" "Concs = 0.344665429" "Concs = 0.433300567"
## [10] "Concs = 0.79823473"  "Concs = 0.910129645" "Concs = 0.789753599"
## [13] "Concs = 1.097803094" "Concs = 1.250836941" "Concs = 0.891346428"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.006856     0.012450  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.235999 -0.032614 -0.006856  0.040146  0.156281 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0068560  0.0371784   0.184    0.857    
## Time[ind]   0.0124499  0.0007341  16.960 3.01e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09186 on 13 degrees of freedom
## Multiple R-squared:  0.9568, Adjusted R-squared:  0.9534 
## F-statistic: 287.6 on 1 and 13 DF,  p-value: 3.008e-10

## (Intercept)   Time[ind] 
##  0.00685602  0.01244988 
##                   2.5 %     97.5 %
## (Intercept) -0.07346298 0.08717502
## Time[ind]    0.01086398 0.01403577
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  61" "Indices =  62" "Indices =  63" "Indices =  64"
##  [5] "Indices =  65" "Indices =  66" "Indices =  67" "Indices =  68"
##  [9] "Indices =  69" "Indices =  70" "Indices =  71" "Indices =  72"
## [13] "Indices =  73"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.660583406" "Concs = 0.521827731" "Concs = 0.519014334"
##  [7] "Concs = 0.937060708" "Concs = 0.947234926" "Concs = 1.586433592"
## [10] "Concs = 1.701961252" "Concs = 2.098184546" "Concs = 2.114078113"
## [13] "Concs = 1.9947066"  
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.15067      0.02247  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.1782 -0.1507  0.0313  0.1123  0.2031 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.150670   0.058446   2.578   0.0257 *  
## Time[ind]   0.022469   0.001143  19.654 6.44e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1406 on 11 degrees of freedom
## Multiple R-squared:  0.9723, Adjusted R-squared:  0.9698 
## F-statistic: 386.3 on 1 and 11 DF,  p-value: 6.445e-10

## (Intercept)   Time[ind] 
##  0.15066966  0.02246945 
##                  2.5 %     97.5 %
## (Intercept) 0.02203109 0.27930823
## Time[ind]   0.01995315 0.02498576
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  0.712"
##  [1] "Indices =  74" "Indices =  75" "Indices =  76" "Indices =  77"
##  [5] "Indices =  78" "Indices =  79" "Indices =  80" "Indices =  81"
##  [9] "Indices =  82" "Indices =  83" "Indices =  84" "Indices =  85"
## [13] "Indices =  86" "Indices =  87"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
##  [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##           0            0  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##      0      0      0      0      0 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)        0          0      NA       NA
## Time[ind]          0          0      NA       NA
## 
## Residual standard error: 0 on 12 degrees of freedom
## Multiple R-squared:    NaN,  Adjusted R-squared:    NaN 
## F-statistic:   NaN on 1 and 12 DF,  p-value: NA

## (Intercept)   Time[ind] 
##           0           0 
##             2.5 % 97.5 %
## (Intercept)     0      0
## Time[ind]       0      0
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  3.1684"
##  [1] "Indices =  88"  "Indices =  89"  "Indices =  90"  "Indices =  91" 
##  [5] "Indices =  92"  "Indices =  93"  "Indices =  94"  "Indices =  95" 
##  [9] "Indices =  96"  "Indices =  97"  "Indices =  98"  "Indices =  99" 
## [13] "Indices =  100" "Indices =  101" "Indices =  102"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [7] "Concs = 0"           "Concs = 0"           "Concs = 0"          
## [10] "Concs = 0.004276181" "Concs = 0"           "Concs = 0"          
## [13] "Concs = 0.068958259" "Concs = 0.095246481" "Concs = 0.042564751"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##  -0.0124160    0.0006791  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.028331 -0.007958  0.002229  0.012416  0.046542 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)   
## (Intercept) -0.0124160  0.0082982  -1.496  0.15847   
## Time[ind]    0.0006791  0.0001638   4.145  0.00115 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0205 on 13 degrees of freedom
## Multiple R-squared:  0.5692, Adjusted R-squared:  0.5361 
## F-statistic: 17.18 on 1 and 13 DF,  p-value: 0.001152

##   (Intercept)     Time[ind] 
## -0.0124160299  0.0006791216 
##                     2.5 %      97.5 %
## (Intercept) -0.0303432318 0.005511172
## Time[ind]    0.0003251496 0.001033094
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  103" "Indices =  104" "Indices =  105" "Indices =  106"
##  [5] "Indices =  107" "Indices =  108" "Indices =  109" "Indices =  110"
##  [9] "Indices =  111" "Indices =  112" "Indices =  113" "Indices =  114"
## [13] "Indices =  115" "Indices =  116" "Indices =  117"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [7] "Concs = 0"           "Concs = 0"           "Concs = 0"          
## [10] "Concs = 0"           "Concs = 0.08814803"  "Concs = 0"          
## [13] "Concs = 0.636612173" "Concs = 0.308057976" "Concs = 0.343301822"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##   -0.076456     0.004313  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.18231 -0.05293  0.01176  0.05403  0.32492 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.076456   0.051227  -1.492 0.159438    
## Time[ind]    0.004313   0.001011   4.264 0.000923 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1266 on 13 degrees of freedom
## Multiple R-squared:  0.5831, Adjusted R-squared:  0.551 
## F-statistic: 18.18 on 1 and 13 DF,  p-value: 0.0009232

##  (Intercept)    Time[ind] 
## -0.076455952  0.004312751 
##                    2.5 %      97.5 %
## (Intercept) -0.187125601 0.034213697
## Time[ind]    0.002127583 0.006497919
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  118" "Indices =  119" "Indices =  120" "Indices =  121"
##  [5] "Indices =  122" "Indices =  123" "Indices =  124" "Indices =  125"
##  [9] "Indices =  126" "Indices =  127" "Indices =  128" "Indices =  129"
## [13] "Indices =  130"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.303186347" "Concs = 0.314346484" "Concs = 0.32890249" 
##  [7] "Concs = 0.470955087" "Concs = 0.418661875" "Concs = 0.69686814" 
## [10] "Concs = 0.65732937"  "Concs = 1.058297138" "Concs = 1.054151944"
## [13] "Concs = 0.826804017"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.08568      0.01013  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.17082 -0.08568  0.02900  0.06552  0.09123 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0856770  0.0366138    2.34   0.0392 *  
## Time[ind]   0.0101327  0.0007162   14.15 2.11e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.08809 on 11 degrees of freedom
## Multiple R-squared:  0.9479, Adjusted R-squared:  0.9432 
## F-statistic: 200.2 on 1 and 11 DF,  p-value: 2.106e-08

## (Intercept)   Time[ind] 
##  0.08567696  0.01013273 
##                   2.5 %     97.5 %
## (Intercept) 0.005090447 0.16626348
## Time[ind]   0.008556376 0.01170909
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  131" "Indices =  132" "Indices =  133" "Indices =  134"
##  [5] "Indices =  135" "Indices =  136" "Indices =  137" "Indices =  138"
##  [9] "Indices =  139" "Indices =  140" "Indices =  141" "Indices =  142"
## [13] "Indices =  143" "Indices =  144" "Indices =  145" "Indices =  146"
## [17] "Indices =  147" "Indices =  148"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15"
##  [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0.651134538" "Concs = 0.410418033"
##  [7] "Concs = 0.72633168"  "Concs = 0.655344167" "Concs = 1.213331632"
## [10] "Concs = 0.938854783" "Concs = 1.336588359" "Concs = 1.220393789"
## [13] "Concs = 2.258618197" "Concs = 2.185187246" "Concs = 2.037689206"
## [16] "Concs = 2.794152863" "Concs = 2.97663412"  "Concs = 2.702787847"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.12001      0.03166  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.26683 -0.12001  0.01248  0.14043  0.26671 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.120012   0.058315   2.058   0.0563 .  
## Time[ind]   0.031662   0.001243  25.467 2.24e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1647 on 16 degrees of freedom
## Multiple R-squared:  0.9759, Adjusted R-squared:  0.9744 
## F-statistic: 648.6 on 1 and 16 DF,  p-value: 2.241e-14

## (Intercept)   Time[ind] 
##  0.12001167  0.03166231 
##                    2.5 %     97.5 %
## (Intercept) -0.003610993 0.24363433
## Time[ind]    0.029026668 0.03429796
## [1] "##################################################"
## 'data.frame':    10 obs. of  2 variables:
##  $ sub: num  50 10 100 75 125 ...
##  $ vel: num  47.2 23.2 127.1 62.2 112.3 ...
##         sub        vel
## 1   50.0000  47.193323
## 2   10.0000  23.197644
## 3  100.0000 127.084516
## 4   75.0000  62.249384
## 5  125.0000 112.347269
## 6    0.7120   0.000000
## 7    3.1684   3.395608
## 8  200.0000  21.563755
## 9  250.0000  50.663660
## 10 150.0000 158.311559

We are interested in the reaction rate, v, which is a function of available substrate (pesticide) and the presence of an enzyme. We get Vmax from the asymptote and K = 0.5*Vmax. Biochemical reactions with a single substrate are typically assumed to follow Michaelis-Menten kinetics even if they deviate from the basic model assumptions.

We are fitting the 2-parameter model.

Used to estimate slopes.

dia

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.17588934"  "Concs = 0.162027282" "Concs = 0.163356559"
##  [7] "Concs = 0.343213005" "Concs = 0.307927387" "Concs = 0.309459105"
## [10] "Concs = 0.560097677" "Concs = 0.54821645"  "Concs = 0.533109282"
## [13] "Concs = 0.73827321"  "Concs = 0.728694143" "Concs = 0.726811372"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.040150     0.008025  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.040150 -0.034677  0.002826  0.026782  0.062303 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0401505  0.0141144   2.845   0.0138 *  
## Time[ind]   0.0080253  0.0002787  28.797 3.67e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03488 on 13 degrees of freedom
## Multiple R-squared:  0.9846, Adjusted R-squared:  0.9834 
## F-statistic: 829.3 on 1 and 13 DF,  p-value: 3.671e-13

## (Intercept)   Time[ind] 
## 0.040150483 0.008025329 
##                   2.5 %      97.5 %
## (Intercept) 0.009658192 0.070642775
## Time[ind]   0.007423260 0.008627398
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.037225886" "Concs = 0.038369499" "Concs = 0.046312162"
##  [7] "Concs = 0.08490015"  "Concs = 0.083838648" "Concs = 0.093345378"
## [10] "Concs = 0.209721193" "Concs = 0.168743119" "Concs = 0.161851994"
## [13] "Concs = 0.162150446" "Concs = 0.222852555" "Concs = 0.229604672"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.004532     0.002650  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.020209 -0.005225 -0.001700  0.001442  0.046169 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0045322  0.0062267   0.728     0.48    
## Time[ind]   0.0026503  0.0001308  20.257 3.23e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01517 on 13 degrees of freedom
## Multiple R-squared:  0.9693, Adjusted R-squared:  0.9669 
## F-statistic: 410.3 on 1 and 13 DF,  p-value: 3.233e-11

## (Intercept)   Time[ind] 
## 0.004532231 0.002650328 
##                    2.5 %      97.5 %
## (Intercept) -0.008919788 0.017984250
## Time[ind]    0.002367676 0.002932981
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.519984026" "Concs = 0.456185794" "Concs = 0.465640368"
##  [7] "Concs = 0.969762496" "Concs = 0.925948373" "Concs = 0.828633383"
## [10] "Concs = 1.646101156" "Concs = 1.493978674" "Concs = 1.273473826"
## [13] "Concs = 2.097846916" "Concs = 1.845660879" "Concs = 1.775884862"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.14326      0.02077  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.23664 -0.14326  0.01084  0.09494  0.25667 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.14326    0.06330   2.263   0.0414 *  
## Time[ind]    0.02077    0.00125  16.617 3.88e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1564 on 13 degrees of freedom
## Multiple R-squared:  0.955,  Adjusted R-squared:  0.9516 
## F-statistic: 276.1 on 1 and 13 DF,  p-value: 3.88e-10

## (Intercept)   Time[ind] 
##  0.14326104  0.02076955 
##                   2.5 %     97.5 %
## (Intercept) 0.006505081 0.28001700
## Time[ind]   0.018069306 0.02346979
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59" "Indices =  60"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.105167732" "Concs = 0.164272494" "Concs = 0.177858813"
##  [7] "Concs = 0.289730134" "Concs = 0.302066953" "Concs = 0.387892352"
## [10] "Concs = 0.703975509" "Concs = 0.8027739"   "Concs = 0.718751156"
## [13] "Concs = 0.974859321" "Concs = 1.104369407" "Concs = 0.769135715"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.003918     0.011012  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.225872 -0.026182 -0.003918  0.046471  0.138129 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0039178  0.0349716   0.112    0.913    
## Time[ind]   0.0110121  0.0006905  15.948 6.47e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.08641 on 13 degrees of freedom
## Multiple R-squared:  0.9514, Adjusted R-squared:  0.9476 
## F-statistic: 254.3 on 1 and 13 DF,  p-value: 6.468e-10

## (Intercept)   Time[ind] 
## 0.003917758 0.011012115 
##                    2.5 %     97.5 %
## (Intercept) -0.071633704 0.07946922
## Time[ind]    0.009520354 0.01250388
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  61" "Indices =  62" "Indices =  63" "Indices =  64"
##  [5] "Indices =  65" "Indices =  66" "Indices =  67" "Indices =  68"
##  [9] "Indices =  69" "Indices =  70" "Indices =  71" "Indices =  72"
## [13] "Indices =  73"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.558156141" "Concs = 0.453398653" "Concs = 0.457441572"
##  [7] "Concs = 0.819739976" "Concs = 0.818340148" "Concs = 1.39707951" 
## [10] "Concs = 1.483198815" "Concs = 1.818559552" "Concs = 1.850457042"
## [13] "Concs = 1.741234977"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.12932      0.01963  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.15472 -0.12932  0.02964  0.10015  0.17613 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.1293156  0.0503960   2.566   0.0262 *  
## Time[ind]   0.0196293  0.0009858  19.912  5.6e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1212 on 11 degrees of freedom
## Multiple R-squared:  0.973,  Adjusted R-squared:  0.9706 
## F-statistic: 396.5 on 1 and 11 DF,  p-value: 5.603e-10

## (Intercept)   Time[ind] 
##   0.1293156   0.0196293 
##                  2.5 %     97.5 %
## (Intercept) 0.01839473 0.24023649
## Time[ind]   0.01745957 0.02179903
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  0.712"
##  [1] "Indices =  74" "Indices =  75" "Indices =  76" "Indices =  77"
##  [5] "Indices =  78" "Indices =  79" "Indices =  80" "Indices =  81"
##  [9] "Indices =  82" "Indices =  83" "Indices =  84" "Indices =  85"
## [13] "Indices =  86" "Indices =  87" "Indices =  88"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
##  [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##           0            0  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##      0      0      0      0      0 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)        0          0      NA       NA
## Time[ind]          0          0      NA       NA
## 
## Residual standard error: 0 on 13 degrees of freedom
## Multiple R-squared:    NaN,  Adjusted R-squared:    NaN 
## F-statistic:   NaN on 1 and 13 DF,  p-value: NA

## (Intercept)   Time[ind] 
##           0           0 
##             2.5 % 97.5 %
## (Intercept)     0      0
## Time[ind]       0      0
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  3.1684"
##  [1] "Indices =  89"  "Indices =  90"  "Indices =  91"  "Indices =  92" 
##  [5] "Indices =  93"  "Indices =  94"  "Indices =  95"  "Indices =  96" 
##  [9] "Indices =  97"  "Indices =  98"  "Indices =  99"  "Indices =  100"
## [13] "Indices =  101" "Indices =  102" "Indices =  103"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
##  [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##           0            0  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##      0      0      0      0      0 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)        0          0      NA       NA
## Time[ind]          0          0      NA       NA
## 
## Residual standard error: 0 on 13 degrees of freedom
## Multiple R-squared:    NaN,  Adjusted R-squared:    NaN 
## F-statistic:   NaN on 1 and 13 DF,  p-value: NA

## (Intercept)   Time[ind] 
##           0           0 
##             2.5 % 97.5 %
## (Intercept)     0      0
## Time[ind]       0      0
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  104" "Indices =  105" "Indices =  106" "Indices =  107"
##  [5] "Indices =  108" "Indices =  109" "Indices =  110" "Indices =  111"
##  [9] "Indices =  112" "Indices =  113" "Indices =  114" "Indices =  115"
## [13] "Indices =  116"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.488073154" "Concs = 0.494203709" "Concs = 0.58569046" 
##  [7] "Concs = 0.731173258" "Concs = 0.714667917" "Concs = 1.145221545"
## [10] "Concs = 1.154181588" "Concs = 1.638731263" "Concs = 1.563749853"
## [13] "Concs = 1.475092589"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.15075      0.01622  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.15075 -0.13584  0.02780  0.09369  0.19157 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.1507544  0.0503259   2.996   0.0122 *  
## Time[ind]   0.0162242  0.0009844  16.481 4.21e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1211 on 11 degrees of freedom
## Multiple R-squared:  0.9611, Adjusted R-squared:  0.9575 
## F-statistic: 271.6 on 1 and 11 DF,  p-value: 4.214e-09

## (Intercept)   Time[ind] 
##   0.1507544   0.0162242 
##                  2.5 %     97.5 %
## (Intercept) 0.03998791 0.26152088
## Time[ind]   0.01405749 0.01839091
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  117" "Indices =  118" "Indices =  119" "Indices =  120"
##  [5] "Indices =  121" "Indices =  122" "Indices =  123" "Indices =  124"
##  [9] "Indices =  125" "Indices =  126" "Indices =  127" "Indices =  128"
## [13] "Indices =  129" "Indices =  130" "Indices =  131" "Indices =  132"
## [17] "Indices =  133" "Indices =  134"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15"
##  [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0.462309631" "Concs = 0.255700106"
##  [7] "Concs = 0.526463046" "Concs = 0.47230486"  "Concs = 0.931548447"
## [10] "Concs = 0.722337549" "Concs = 1.066740758" "Concs = 0.948249061"
## [13] "Concs = 1.827879364" "Concs = 1.789768545" "Concs = 1.614786398"
## [16] "Concs = 2.243971727" "Concs = 2.385364241" "Concs = 2.16439478" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.06633      0.02574  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.21878 -0.06632  0.00304  0.08820  0.22813 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.066325   0.048063    1.38    0.187    
## Time[ind]   0.025743   0.001025   25.12 2.77e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1357 on 16 degrees of freedom
## Multiple R-squared:  0.9753, Adjusted R-squared:  0.9737 
## F-statistic: 631.1 on 1 and 16 DF,  p-value: 2.773e-14

## (Intercept)   Time[ind] 
##   0.0663253   0.0257428 
##                   2.5 %     97.5 %
## (Intercept) -0.03556328 0.16821388
## Time[ind]    0.02357053 0.02791507
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  135" "Indices =  136" "Indices =  137" "Indices =  138"
##  [5] "Indices =  139" "Indices =  140" "Indices =  141" "Indices =  142"
##  [9] "Indices =  143" "Indices =  144" "Indices =  145" "Indices =  146"
## [13] "Indices =  147" "Indices =  148" "Indices =  149"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [7] "Concs = 0"           "Concs = 0"           "Concs = 0"          
## [10] "Concs = 0.147179292" "Concs = 0.49374336"  "Concs = 0.185151589"
## [13] "Concs = 0.905020781" "Concs = 0.751527127" "Concs = 0.778803003"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##   -0.135092     0.009039  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.260068 -0.136078 -0.000493  0.117739  0.226604 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.135092   0.061636  -2.192   0.0472 *  
## Time[ind]    0.009039   0.001217   7.427 4.99e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1523 on 13 degrees of freedom
## Multiple R-squared:  0.8093, Adjusted R-squared:  0.7946 
## F-statistic: 55.16 on 1 and 13 DF,  p-value: 4.994e-06

##  (Intercept)    Time[ind] 
## -0.135091948  0.009038982 
##                    2.5 %       97.5 %
## (Intercept) -0.268247657 -0.001936239
## Time[ind]    0.006409827  0.011668136
## [1] "##################################################"
## 'data.frame':    10 obs. of  2 variables:
##  $ sub: num  50 10 100 75 125 ...
##  $ vel: num  40.1 13.3 103.8 55.1 98.1 ...
##         sub       vel
## 1   50.0000  40.12665
## 2   10.0000  13.25164
## 3  100.0000 103.84774
## 4   75.0000  55.06057
## 5  125.0000  98.14650
## 6    0.7120   0.00000
## 7    3.1684   0.00000
## 8  250.0000  81.12099
## 9  150.0000 128.71399
## 10 200.0000  45.19491

triadimefon

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  0.68082"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.491983075" "Concs = 0.401196591" "Concs = 0.426789449"
##  [4] "Concs = 0.399443695" "Concs = 0.42224169"  "Concs = 0.36799564" 
##  [7] "Concs = 0.335043095" "Concs = 0.307545884" "Concs = 0.33049829" 
## [10] "Concs = 0.298781298" "Concs = 0.300851183" "Concs = 0.297372843"
## [13] "Concs = 0.30988245"  "Concs = 0.29724505"  "Concs = 0.293730776"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.411830    -0.001533  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.05829 -0.02177 -0.01063  0.02164  0.08015 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.4118302  0.0148783  27.680 6.09e-13 ***
## Time[ind]   -0.0015331  0.0002938  -5.219 0.000166 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03676 on 13 degrees of freedom
## Multiple R-squared:  0.6769, Adjusted R-squared:  0.652 
## F-statistic: 27.23 on 1 and 13 DF,  p-value: 0.0001656

##  (Intercept)    Time[ind] 
##  0.411830209 -0.001533081 
##                    2.5 %        97.5 %
## (Intercept)  0.379687608  0.4439728100
## Time[ind]   -0.002167735 -0.0008984261
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 1.66496797"  "Concs = 1.809450976" "Concs = 2.047584443"
##  [4] "Concs = 3.796829723" "Concs = 3.995422538" "Concs = 4.084402023"
##  [7] "Concs = 3.689670522" "Concs = 3.770627455" "Concs = 3.708045842"
## [10] "Concs = 2.923805377" "Concs = 2.81999575"  "Concs = 1.627429272"
## [13] "Concs = 1.556106647" "Concs = 1.615639352"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     3.23029     -0.01165  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.5653 -0.6112  0.3404  0.8225  1.0288 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.230286   0.400694   8.062 3.48e-06 ***
## Time[ind]   -0.011646   0.008028  -1.451    0.173    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9894 on 12 degrees of freedom
## Multiple R-squared:  0.1492, Adjusted R-squared:  0.07829 
## F-statistic: 2.104 on 1 and 12 DF,  p-value: 0.1725

## (Intercept)   Time[ind] 
##  3.23028639 -0.01164577 
##                   2.5 %      97.5 %
## (Intercept)  2.35724967 4.103323110
## Time[ind]   -0.02913777 0.005846224
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  30" "Indices =  31" "Indices =  32" "Indices =  33"
##  [5] "Indices =  34" "Indices =  35" "Indices =  36" "Indices =  37"
##  [9] "Indices =  38" "Indices =  39" "Indices =  40" "Indices =  41"
## [13] "Indices =  42" "Indices =  43" "Indices =  44"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.953124823" "Concs = 0.851227037" "Concs = 0.735830293"
##  [4] "Concs = 1.438977536" "Concs = 1.147878572" "Concs = 1.273836719"
##  [7] "Concs = 1.170628317" "Concs = 1.153347335" "Concs = 0.90609785" 
## [10] "Concs = 0.796555881" "Concs = 0.724314066" "Concs = 0.705525399"
## [13] "Concs = 0.684015583" "Concs = 0.645877009" "Concs = 0.633912406"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    1.105417    -0.004718  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.36959 -0.10741 -0.03491  0.15135  0.40433 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.105417   0.084540  13.076 7.41e-09 ***
## Time[ind]   -0.004718   0.001669  -2.827   0.0143 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2089 on 13 degrees of freedom
## Multiple R-squared:  0.3806, Adjusted R-squared:  0.333 
## F-statistic: 7.989 on 1 and 13 DF,  p-value: 0.01429

##  (Intercept)    Time[ind] 
##  1.105417292 -0.004718138 
##                    2.5 %      97.5 %
## (Intercept)  0.922779946  1.28805464
## Time[ind]   -0.008324305 -0.00111197
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  45" "Indices =  46" "Indices =  47" "Indices =  48"
##  [5] "Indices =  49" "Indices =  50" "Indices =  51" "Indices =  52"
##  [9] "Indices =  53" "Indices =  54" "Indices =  55" "Indices =  56"
## [13] "Indices =  57"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 24.40802225" "Concs = 24.82657815" "Concs = 23.72724558"
##  [4] "Concs = 25.6223204"  "Concs = 24.15898057" "Concs = 24.97516518"
##  [7] "Concs = 26.62994332" "Concs = 26.25228145" "Concs = 25.95782864"
## [10] "Concs = 28.59868326" "Concs = 22.32352998" "Concs = 22.61126729"
## [13] "Concs = 22.93204565"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    25.37794     -0.01392  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8018 -1.1933 -0.5514  1.2919  4.0558 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 25.37794    0.74253  34.178 1.61e-12 ***
## Time[ind]   -0.01392    0.01452  -0.958    0.359    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.786 on 11 degrees of freedom
## Multiple R-squared:  0.07704,    Adjusted R-squared:  -0.006863 
## F-statistic: 0.9182 on 1 and 11 DF,  p-value: 0.3585

## (Intercept)   Time[ind] 
## 25.37794389 -0.01391794 
##                   2.5 %      97.5 %
## (Intercept) 23.74364659 27.01224120
## Time[ind]   -0.04588649  0.01805062
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  58" "Indices =  59" "Indices =  60" "Indices =  61"
##  [5] "Indices =  62" "Indices =  63" "Indices =  64" "Indices =  65"
##  [9] "Indices =  66" "Indices =  67" "Indices =  68" "Indices =  69"
## [13] "Indices =  70" "Indices =  71" "Indices =  72"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 40.78378417" "Concs = 39.14533446" "Concs = 37.19980911"
##  [4] "Concs = 39.60290919" "Concs = 36.37647057" "Concs = 38.41537648"
##  [7] "Concs = 41.36228948" "Concs = 39.60347726" "Concs = 37.05197615"
## [10] "Concs = 38.79077057" "Concs = 39.14694989" "Concs = 38.88285882"
## [13] "Concs = 38.84162326" "Concs = 38.38496898" "Concs = 38.08875118"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    38.88146     -0.00264  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.4654 -0.4908  0.1598  0.5925  2.5600 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 38.88146    0.55263  70.357   <2e-16 ***
## Time[ind]   -0.00264    0.01091  -0.242    0.813    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.365 on 13 degrees of freedom
## Multiple R-squared:  0.004484,   Adjusted R-squared:  -0.07209 
## F-statistic: 0.05855 on 1 and 13 DF,  p-value: 0.8126

##  (Intercept)    Time[ind] 
## 38.881462270 -0.002640315 
##                   2.5 %     97.5 %
## (Intercept) 37.68758232 40.0753422
## Time[ind]   -0.02621343  0.0209328
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  73" "Indices =  74" "Indices =  75" "Indices =  76"
##  [5] "Indices =  77" "Indices =  78" "Indices =  79" "Indices =  80"
##  [9] "Indices =  81" "Indices =  82" "Indices =  83" "Indices =  84"
## [13] "Indices =  85" "Indices =  86" "Indices =  87"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 48.8233658"  "Concs = 45.64682255" "Concs = 49.68642703"
##  [4] "Concs = 49.24893567" "Concs = 52.23999837" "Concs = 54.94800062"
##  [7] "Concs = 51.63283427" "Concs = 55.62979138" "Concs = 53.25296347"
## [10] "Concs = 57.2285182"  "Concs = 52.25557462" "Concs = 57.56142454"
## [13] "Concs = 55.15134637" "Concs = 52.80788424" "Concs = 54.77096052"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    50.27020      0.06296  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.6234 -1.6195 -0.5838  2.1373  3.7334 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 50.27020    1.08609  46.286 8.14e-16 ***
## Time[ind]    0.06296    0.02144   2.936   0.0116 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.684 on 13 degrees of freedom
## Multiple R-squared:  0.3987, Adjusted R-squared:  0.3524 
## F-statistic:  8.62 on 1 and 13 DF,  p-value: 0.01158

## (Intercept)   Time[ind] 
## 50.27019838  0.06296046 
##                   2.5 %     97.5 %
## (Intercept) 47.92384633 52.6165504
## Time[ind]    0.01663183  0.1092891
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  88"  "Indices =  89"  "Indices =  90"  "Indices =  91" 
##  [5] "Indices =  92"  "Indices =  93"  "Indices =  94"  "Indices =  95" 
##  [9] "Indices =  96"  "Indices =  97"  "Indices =  98"  "Indices =  99" 
## [13] "Indices =  100" "Indices =  101"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 61.59837616" "Concs = 58.92902388" "Concs = 62.18995319"
##  [4] "Concs = 54.97761564" "Concs = 64.19295623" "Concs = 61.97688614"
##  [7] "Concs = 68.89112849" "Concs = 56.33566744" "Concs = 71.31751913"
## [10] "Concs = 66.04862513" "Concs = 69.71262134" "Concs = 57.48171016"
## [13] "Concs = 60.79276739" "Concs = 57.42314849"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##   62.580107    -0.008102  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.4810 -4.1897 -0.7317  3.3996  8.9805 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 62.580107   2.177110  28.745 1.95e-12 ***
## Time[ind]   -0.008102   0.043620  -0.186    0.856    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.376 on 12 degrees of freedom
## Multiple R-squared:  0.002867,   Adjusted R-squared:  -0.08023 
## F-statistic: 0.0345 on 1 and 12 DF,  p-value: 0.8558

##  (Intercept)    Time[ind] 
## 62.580106621 -0.008101893 
##                  2.5 %      97.5 %
## (Intercept) 57.8365915 67.32362176
## Time[ind]   -0.1031421  0.08693828
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  102" "Indices =  103" "Indices =  104" "Indices =  105"
##  [5] "Indices =  106" "Indices =  107" "Indices =  108" "Indices =  109"
##  [9] "Indices =  110" "Indices =  111" "Indices =  112" "Indices =  113"
## [13] "Indices =  114" "Indices =  115"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 15"
##  [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 65.77539856" "Concs = 67.99385172" "Concs = 78.63355587"
##  [4] "Concs = 62.93987056" "Concs = 106.7018113" "Concs = 73.37624336"
##  [7] "Concs = 66.9635187"  "Concs = 95.5133834"  "Concs = 69.7678651" 
## [10] "Concs = 58.53815945" "Concs = 61.06336245" "Concs = 82.43537943"
## [13] "Concs = 75.76324133" "Concs = 73.77914496"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    75.38048     -0.02749  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -15.193  -9.102  -2.571   3.463  31.734 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 75.38048    6.14976  12.257 3.82e-08 ***
## Time[ind]   -0.02749    0.11731  -0.234    0.819    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.9 on 12 degrees of freedom
## Multiple R-squared:  0.004555,   Adjusted R-squared:  -0.0784 
## F-statistic: 0.05492 on 1 and 12 DF,  p-value: 0.8187

## (Intercept)   Time[ind] 
## 75.38047797 -0.02749044 
##                  2.5 %     97.5 %
## (Intercept) 61.9813052 88.7796507
## Time[ind]   -0.2830856  0.2281048
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  116" "Indices =  117" "Indices =  118" "Indices =  119"
##  [5] "Indices =  120" "Indices =  121" "Indices =  122" "Indices =  123"
##  [9] "Indices =  124" "Indices =  125" "Indices =  126" "Indices =  127"
## [13] "Indices =  128" "Indices =  129" "Indices =  130"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 293.4352803" "Concs = 357.1944002" "Concs = 335.0321393"
##  [4] "Concs = 338.7826757" "Concs = 357.9520843" "Concs = 202.0964578"
##  [7] "Concs = 422.3552358" "Concs = 340.5253492" "Concs = 345.8291382"
## [10] "Concs = 359.4674526" "Concs = 377.2730298" "Concs = 186.1093226"
## [13] "Concs = 471.6047045" "Concs = 376.1365036" "Concs = 190.6933116"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      324.45         0.15  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -147.34  -10.22   16.88   35.47  133.66 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 324.4495    34.2770   9.466 3.39e-07 ***
## Time[ind]     0.1500     0.6768   0.222    0.828    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 84.69 on 13 degrees of freedom
## Multiple R-squared:  0.003764,   Adjusted R-squared:  -0.07287 
## F-statistic: 0.04911 on 1 and 13 DF,  p-value: 0.8281

## (Intercept)   Time[ind] 
##  324.449491    0.149991 
##                  2.5 %     97.5 %
## (Intercept) 250.398438 398.500544
## Time[ind]    -1.312144   1.612126
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  131" "Indices =  132" "Indices =  133" "Indices =  134"
##  [5] "Indices =  135" "Indices =  136" "Indices =  137" "Indices =  138"
##  [9] "Indices =  139" "Indices =  140" "Indices =  141" "Indices =  142"
## [13] "Indices =  143" "Indices =  144"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 15"
##  [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 222.4579985" "Concs = 180.8725406" "Concs = 186.8824662"
##  [4] "Concs = 208.9457498" "Concs = 167.0779465" "Concs = 229.5166359"
##  [7] "Concs = 99.11335239" "Concs = 263.0350796" "Concs = 59.52448054"
## [10] "Concs = 46.29054385" "Concs = 51.98182232" "Concs = 162.0360626"
## [13] "Concs = 200.5560551" "Concs = 187.8908429"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    190.1312      -0.6763  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -103.26  -56.27   17.93   52.17   93.19 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 190.1312    30.5866   6.216 4.48e-05 ***
## Time[ind]    -0.6763     0.5835  -1.159    0.269    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 69.11 on 12 degrees of freedom
## Multiple R-squared:  0.1007, Adjusted R-squared:  0.02576 
## F-statistic: 1.344 on 1 and 12 DF,  p-value: 0.2689

## (Intercept)   Time[ind] 
##  190.131172   -0.676333 
##                  2.5 %      97.5 %
## (Intercept) 123.488657 256.7736868
## Time[ind]    -1.947569   0.5949027
## [1] "##################################################"
## 'data.frame':    10 obs. of  2 variables:
##  $ sub: num  0.681 10 2.89 50 75 ...
##  $ vel: num  7.67 58.23 23.59 69.59 13.2 ...
##          sub         vel
## 1    0.68082    7.665403
## 2   10.00000   58.228872
## 3    2.89000   23.590688
## 4   50.00000   69.589686
## 5   75.00000   13.201577
## 6  100.00000 -314.802324
## 7  125.00000   40.509466
## 8  150.00000  137.452183
## 9  200.00000 -749.954886
## 10 250.00000 3381.665221

tdla

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  0.68"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.776869584" "Concs = 0.395237886" "Concs = 2.220388898"
##  [4] "Concs = 0.124349504" "Concs = 0.14627783"  "Concs = 0.089752887"
##  [7] "Concs = 0.107638677" "Concs = 0.159434476" "Concs = 0.159787554"
## [10] "Concs = 0.099828091" "Concs = 0.225228369" "Concs = 0.139329405"
## [13] "Concs = 0.072482112" "Concs = 0.09994686"  "Concs = 0.061506341"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.631813    -0.007862  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.42413 -0.26245 -0.06028  0.14115  1.58858 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  0.631813   0.205207   3.079   0.0088 **
## Time[ind]   -0.007862   0.004052  -1.940   0.0743 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.507 on 13 degrees of freedom
## Multiple R-squared:  0.2246, Adjusted R-squared:  0.1649 
## F-statistic: 3.765 on 1 and 13 DF,  p-value: 0.07434

##  (Intercept)    Time[ind] 
##  0.631813196 -0.007861777 
##                   2.5 %       97.5 %
## (Intercept)  0.18849145 1.0751349430
## Time[ind]   -0.01661515 0.0008915944
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.964686974" "Concs = 0.95171618"  "Concs = 0.951349197"
##  [4] "Concs = 0.562008549" "Concs = 0.514503123" "Concs = 0.553400833"
##  [7] "Concs = 0.914781067" "Concs = 0.896944628" "Concs = 0.854682343"
## [10] "Concs = 0.640465968" "Concs = 1.46510307"  "Concs = 1.529173181"
## [13] "Concs = 1.670981262" "Concs = 1.594325825" "Concs = 1.598291535"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.672054     0.009541  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.60406 -0.17839  0.06356  0.24994  0.29263 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.672054   0.112477   5.975 4.63e-05 ***
## Time[ind]   0.009541   0.002221   4.296 0.000869 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2779 on 13 degrees of freedom
## Multiple R-squared:  0.5867, Adjusted R-squared:  0.555 
## F-statistic: 18.46 on 1 and 13 DF,  p-value: 0.0008694

## (Intercept)   Time[ind] 
## 0.672054090 0.009541201 
##                   2.5 %     97.5 %
## (Intercept) 0.429063247 0.91504493
## Time[ind]   0.004743356 0.01433905
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90"
##  [1] "Concs = 0.504235051" "Concs = 0.597387774" "Concs = 0.684729101"
##  [4] "Concs = 0.587769932" "Concs = 0.500911907" "Concs = 2.390614252"
##  [7] "Concs = 0.732569141" "Concs = 0.819349521" "Concs = 0.882196657"
## [10] "Concs = 1.272480799" "Concs = 1.332879865" "Concs = 1.171215513"
## [13] "Concs = 1.284978616" "Concs = 1.466507839"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.751543     0.007487  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.36294 -0.22190 -0.11719  0.02344  1.52676 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 0.751543   0.197099   3.813  0.00247 **
## Time[ind]   0.007487   0.004231   1.769  0.10220   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4801 on 12 degrees of freedom
## Multiple R-squared:  0.2069, Adjusted R-squared:  0.1408 
## F-statistic: 3.131 on 1 and 12 DF,  p-value: 0.1022

## (Intercept)   Time[ind] 
## 0.751542759 0.007487328 
##                    2.5 %     97.5 %
## (Intercept)  0.322101740 1.18098378
## Time[ind]   -0.001732215 0.01670687
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  45" "Indices =  46" "Indices =  47" "Indices =  48"
##  [5] "Indices =  49" "Indices =  50" "Indices =  51" "Indices =  52"
##  [9] "Indices =  53" "Indices =  54" "Indices =  55" "Indices =  56"
## [13] "Indices =  57" "Indices =  58" "Indices =  59"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 4.958654666" "Concs = 5.087523701" "Concs = 4.465832565"
##  [4] "Concs = 2.366202494" "Concs = 2.316676352" "Concs = 2.98040696" 
##  [7] "Concs = 2.746818134" "Concs = 3.431666105" "Concs = 3.294563534"
## [10] "Concs = 3.820882667" "Concs = 4.627112685" "Concs = 4.219456142"
## [13] "Concs = 4.7035697"   "Concs = 4.419483485" "Concs = 4.677842802"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    3.538943     0.008603  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.3513 -0.5950  0.1063  0.4812  1.5486 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 3.538943   0.380001   9.313 4.08e-07 ***
## Time[ind]   0.008603   0.007503   1.147    0.272    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9389 on 13 degrees of freedom
## Multiple R-squared:  0.09183,    Adjusted R-squared:  0.02198 
## F-statistic: 1.315 on 1 and 13 DF,  p-value: 0.2722

## (Intercept)   Time[ind] 
## 3.538942877 0.008602648 
##                    2.5 %     97.5 %
## (Intercept)  2.718000761 4.35988499
## Time[ind]   -0.007606824 0.02481212
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  60" "Indices =  61" "Indices =  62" "Indices =  63"
##  [5] "Indices =  64" "Indices =  65" "Indices =  66" "Indices =  67"
##  [9] "Indices =  68" "Indices =  69" "Indices =  70" "Indices =  71"
## [13] "Indices =  72" "Indices =  73" "Indices =  74"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 2.568919585" "Concs = 2.306987426" "Concs = 2.580318005"
##  [4] "Concs = 2.219185884" "Concs = 2.155328801" "Concs = 2.202708256"
##  [7] "Concs = 2.811019032" "Concs = 2.229132105" "Concs = 2.319209877"
## [10] "Concs = 3.438186485" "Concs = 3.239731804" "Concs = 3.112249253"
## [13] "Concs = 3.973569475" "Concs = 3.922150065" "Concs = 3.990347195"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     2.13186      0.01896  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.47150 -0.20530  0.08396  0.16046  0.44846 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.13186    0.11545  18.465 1.04e-10 ***
## Time[ind]    0.01896    0.00228   8.317 1.46e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2853 on 13 degrees of freedom
## Multiple R-squared:  0.8418, Adjusted R-squared:  0.8296 
## F-statistic: 69.17 on 1 and 13 DF,  p-value: 1.458e-06

## (Intercept)   Time[ind] 
##  2.13185708  0.01895929 
##                  2.5 %     97.5 %
## (Intercept) 1.88244004 2.38127412
## Time[ind]   0.01403456 0.02388402
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  75" "Indices =  76" "Indices =  77" "Indices =  78"
##  [5] "Indices =  79" "Indices =  80" "Indices =  81" "Indices =  82"
##  [9] "Indices =  83" "Indices =  84" "Indices =  85" "Indices =  86"
## [13] "Indices =  87" "Indices =  88" "Indices =  89"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 3.426769825" "Concs = 4.801627038" "Concs = 5.167321476"
##  [4] "Concs = 2.973173898" "Concs = 4.278761105" "Concs = 5.203600328"
##  [7] "Concs = 3.752087918" "Concs = 4.489689601" "Concs = 4.3820044"  
## [10] "Concs = 4.18858056"  "Concs = 4.787062374" "Concs = 4.819935077"
## [13] "Concs = 5.229225315" "Concs = 5.541134166" "Concs = 5.363637277"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     4.11811      0.01134  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.31501 -0.34305  0.02152  0.31381  1.04922 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.118105   0.268274  15.350 1.04e-09 ***
## Time[ind]   0.011339   0.005297   2.141   0.0518 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6629 on 13 degrees of freedom
## Multiple R-squared:  0.2606, Adjusted R-squared:  0.2037 
## F-statistic: 4.582 on 1 and 13 DF,  p-value: 0.05185

## (Intercept)   Time[ind] 
##  4.11810545  0.01133851 
##                     2.5 %     97.5 %
## (Intercept)  3.5385341200 4.69767679
## Time[ind]   -0.0001051039 0.02278212
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  90"  "Indices =  91"  "Indices =  92"  "Indices =  93" 
##  [5] "Indices =  94"  "Indices =  95"  "Indices =  96"  "Indices =  97" 
##  [9] "Indices =  98"  "Indices =  99"  "Indices =  100" "Indices =  101"
## [13] "Indices =  102" "Indices =  103" "Indices =  104"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 2.777271491" "Concs = 5.313869486" "Concs = 5.064521305"
##  [4] "Concs = 3.664975002" "Concs = 5.128116042" "Concs = 3.342678541"
##  [7] "Concs = 3.909877303" "Concs = 3.131834777" "Concs = 6.184369077"
## [10] "Concs = 5.034115174" "Concs = 6.997125798" "Concs = 5.513028895"
## [13] "Concs = 5.609126979" "Concs = 6.565737598" "Concs = 6.051117386"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     4.01963      0.02392  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.6054 -0.7704 -0.1213  0.8973  1.5423 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.019629   0.432639   9.291 4.19e-07 ***
## Time[ind]   0.023920   0.008542   2.800    0.015 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.069 on 13 degrees of freedom
## Multiple R-squared:  0.3762, Adjusted R-squared:  0.3282 
## F-statistic: 7.841 on 1 and 13 DF,  p-value: 0.01503

## (Intercept)   Time[ind] 
##  4.01962890  0.02392022 
##                   2.5 %     97.5 %
## (Intercept) 3.084968118 4.95428967
## Time[ind]   0.005465383 0.04237507
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  105" "Indices =  106" "Indices =  107" "Indices =  108"
##  [5] "Indices =  109" "Indices =  110" "Indices =  111" "Indices =  112"
##  [9] "Indices =  113" "Indices =  114" "Indices =  115" "Indices =  116"
## [13] "Indices =  117" "Indices =  118" "Indices =  119"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 4.971974528" "Concs = 4.282559204" "Concs = 4.289935015"
##  [4] "Concs = 4.690841414" "Concs = 4.417155339" "Concs = 6.21277087" 
##  [7] "Concs = 3.839544319" "Concs = 4.519625245" "Concs = 6.760429619"
## [10] "Concs = 7.2240805"   "Concs = 3.468203577" "Concs = 4.462789205"
## [13] "Concs = 8.035064896" "Concs = 8.748204845" "Concs = 7.504701282"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     4.25455      0.03352  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.79759 -0.54038  0.03538  0.86097  1.50026 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.25455    0.53109   8.011  2.2e-06 ***
## Time[ind]    0.03352    0.01049   3.197  0.00701 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.312 on 13 degrees of freedom
## Multiple R-squared:  0.4401, Adjusted R-squared:  0.397 
## F-statistic: 10.22 on 1 and 13 DF,  p-value: 0.007014

## (Intercept)   Time[ind] 
##  4.25455185  0.03352069 
##                  2.5 %     97.5 %
## (Intercept) 3.10719564 5.40190806
## Time[ind]   0.01086618 0.05617519
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  120" "Indices =  121" "Indices =  122" "Indices =  123"
##  [5] "Indices =  124" "Indices =  125" "Indices =  126" "Indices =  127"
##  [9] "Indices =  128" "Indices =  129" "Indices =  130"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 30"
##  [6] "Times = 30" "Times = 60" "Times = 60" "Times = 60" "Times = 90"
## [11] "Times = 90"
##  [1] "Concs = 13.83186168" "Concs = 18.22611755" "Concs = 17.81066063"
##  [4] "Concs = 14.08273374" "Concs = 20.76679639" "Concs = 16.9957259" 
##  [7] "Concs = 18.08230553" "Concs = 16.51635254" "Concs = 17.9065353" 
## [10] "Concs = 19.61630031" "Concs = 17.39520371"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    16.36742      0.02486  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.6576 -1.2765  0.0472  1.0407  3.6534 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 16.36742    0.98771  16.571 4.74e-08 ***
## Time[ind]    0.02486    0.01915   1.298    0.227    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.994 on 9 degrees of freedom
## Multiple R-squared:  0.1577, Adjusted R-squared:  0.06412 
## F-statistic: 1.685 on 1 and 9 DF,  p-value: 0.2265

## (Intercept)   Time[ind] 
##  16.3674152   0.0248645 
##                   2.5 %      97.5 %
## (Intercept) 14.13306576 18.60176454
## Time[ind]   -0.01846508  0.06819408
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  0.68 10 2.89 50 75 100 125 150 250
##  $ vel: num  -39.3 47.7 37.4 43 94.8 ...
##      sub       vel
## 1   0.68 -39.30888
## 2  10.00  47.70600
## 3   2.89  37.43664
## 4  50.00  43.01324
## 5  75.00  94.79647
## 6 100.00  56.69255
## 7 125.00 119.60112
## 8 150.00 167.60344
## 9 250.00 124.32252

tdlb

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  0.68"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.285757105" "Concs = 0.146483192" "Concs = 0.792173926"
##  [4] "Concs = 0.159849035" "Concs = 0.171671782" "Concs = 0.137258352"
##  [7] "Concs = 0.135498718" "Concs = 0.166579942" "Concs = 0.160555121"
## [10] "Concs = 0.085155894" "Concs = 0.137641779" "Concs = 0.101223849"
## [13] "Concs = 0.041122976" "Concs = 0.056120989" "Concs = 0.040770384"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.29736     -0.00315  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.15088 -0.07291 -0.02323  0.02705  0.49481 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.297360   0.062206   4.780 0.000359 ***
## Time[ind]   -0.003150   0.001228  -2.564 0.023545 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1537 on 13 degrees of freedom
## Multiple R-squared:  0.3359, Adjusted R-squared:  0.2848 
## F-statistic: 6.576 on 1 and 13 DF,  p-value: 0.02354

##  (Intercept)    Time[ind] 
##  0.297360194 -0.003149641 
##                    2.5 %        97.5 %
## (Intercept)  0.162973379  0.4317470094
## Time[ind]   -0.005803103 -0.0004961782
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.525255948" "Concs = 0.525187009" "Concs = 0.531029336"
##  [4] "Concs = 0.540578005" "Concs = 0.535327972" "Concs = 0.549947891"
##  [7] "Concs = 0.963906807" "Concs = 0.939249694" "Concs = 0.8832653"  
## [10] "Concs = 0.462660817" "Concs = 1.424227752" "Concs = 1.466547242"
## [13] "Concs = 1.470094516" "Concs = 1.424845158" "Concs = 1.471282702"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.49752      0.01068  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.67595 -0.07108  0.02767  0.09319  0.32794 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.497520   0.095950   5.185 0.000176 ***
## Time[ind]   0.010685   0.001895   5.640 8.07e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2371 on 13 degrees of freedom
## Multiple R-squared:  0.7099, Adjusted R-squared:  0.6876 
## F-statistic: 31.81 on 1 and 13 DF,  p-value: 8.067e-05

## (Intercept)   Time[ind] 
##  0.49752033  0.01068479 
##                   2.5 %     97.5 %
## (Intercept) 0.290232188 0.70480848
## Time[ind]   0.006591892 0.01477768
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.200115219" "Concs = 0.242152252" "Concs = 0.309582528"
##  [4] "Concs = 0.502687773" "Concs = 0.443748362" "Concs = 1.739413295"
##  [7] "Concs = 0.631006803" "Concs = 0.676925019" "Concs = 0.712219102"
## [10] "Concs = 0.887492395" "Concs = 0.922424215" "Concs = 0.774293903"
## [13] "Concs = 0.733501521" "Concs = 0.837366651" "Concs = 0.76078022" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.539121     0.003909  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.33901 -0.15573 -0.05358  0.03817  1.14165 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 0.539121   0.145307   3.710  0.00262 **
## Time[ind]   0.003909   0.002869   1.363  0.19617   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.359 on 13 degrees of freedom
## Multiple R-squared:  0.125,  Adjusted R-squared:  0.05765 
## F-statistic: 1.856 on 1 and 13 DF,  p-value: 0.1962

## (Intercept)   Time[ind] 
## 0.539120517 0.003909233 
##                    2.5 %     97.5 %
## (Intercept)  0.225202898 0.85303814
## Time[ind]   -0.002289058 0.01010752
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59" "Indices =  60"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 3.951483646" "Concs = 3.997004582" "Concs = 3.271884585"
##  [4] "Concs = 2.598887073" "Concs = 2.355603277" "Concs = 3.141649164"
##  [7] "Concs = 3.674320887" "Concs = 4.289723095" "Concs = 4.280136564"
## [10] "Concs = 6.243599629" "Concs = 6.734010485" "Concs = 6.361017452"
## [13] "Concs = 7.195467955" "Concs = 6.834134189" "Concs = 6.9532999"  
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     2.96383      0.04688  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.31143 -0.43714 -0.08051  0.52568  1.03317 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.963831   0.305847   9.691 2.59e-07 ***
## Time[ind]   0.046880   0.006039   7.763 3.10e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7557 on 13 degrees of freedom
## Multiple R-squared:  0.8226, Adjusted R-squared:  0.8089 
## F-statistic: 60.26 on 1 and 13 DF,  p-value: 3.103e-06

## (Intercept)   Time[ind] 
##  2.96383098  0.04687993 
##                  2.5 %     97.5 %
## (Intercept) 2.30308946 3.62457250
## Time[ind]   0.03383361 0.05992624
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  61" "Indices =  62" "Indices =  63" "Indices =  64"
##  [5] "Indices =  65" "Indices =  66" "Indices =  67" "Indices =  68"
##  [9] "Indices =  69" "Indices =  70" "Indices =  71" "Indices =  72"
## [13] "Indices =  73" "Indices =  74" "Indices =  75"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 1.941666948" "Concs = 1.681717791" "Concs = 1.73936846" 
##  [4] "Concs = 2.526757358" "Concs = 2.313637237" "Concs = 2.49086012" 
##  [7] "Concs = 3.789628052" "Concs = 3.174642429" "Concs = 3.191438558"
## [10] "Concs = 5.432233942" "Concs = 4.969157891" "Concs = 5.064503301"
## [13] "Concs = 6.712664257" "Concs = 6.597464296" "Concs = 6.484914"   
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     1.73768      0.05478  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.24572 -0.12656 -0.05524  0.04251  0.40859 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.73768    0.08458   20.55  2.7e-11 ***
## Time[ind]    0.05478    0.00167   32.80  6.9e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.209 on 13 degrees of freedom
## Multiple R-squared:  0.9881, Adjusted R-squared:  0.9871 
## F-statistic:  1076 on 1 and 13 DF,  p-value: 6.901e-14

## (Intercept)   Time[ind] 
##  1.73768018  0.05477855 
##                  2.5 %     97.5 %
## (Intercept) 1.55496133 1.92039902
## Time[ind]   0.05117077 0.05838633
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  76" "Indices =  77" "Indices =  78" "Indices =  79"
##  [5] "Indices =  80" "Indices =  81" "Indices =  82" "Indices =  83"
##  [9] "Indices =  84" "Indices =  85" "Indices =  86" "Indices =  87"
## [13] "Indices =  88" "Indices =  89" "Indices =  90"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 2.204827173" "Concs = 3.695255037" "Concs = 4.217693628"
##  [4] "Concs = 2.987986855" "Concs = 4.62322369"  "Concs = 5.738654903"
##  [7] "Concs = 5.010985215" "Concs = 6.920302664" "Concs = 6.308852644"
## [10] "Concs = 8.11715413"  "Concs = 8.804687457" "Concs = 8.950282552"
## [13] "Concs = 10.81651263" "Concs = 11.45788264" "Concs = 11.01782631"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     3.33269      0.08698  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.6494 -0.3892  0.2534  0.3829  1.1013 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 3.332689   0.331419   10.06 1.69e-07 ***
## Time[ind]   0.086977   0.006544   13.29 6.08e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8189 on 13 degrees of freedom
## Multiple R-squared:  0.9315, Adjusted R-squared:  0.9262 
## F-statistic: 176.7 on 1 and 13 DF,  p-value: 6.077e-09

## (Intercept)   Time[ind] 
##  3.33268858  0.08697743 
##                 2.5 %    97.5 %
## (Intercept) 2.6167016 4.0486755
## Time[ind]   0.0728403 0.1011146
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  91"  "Indices =  92"  "Indices =  93"  "Indices =  94" 
##  [5] "Indices =  95"  "Indices =  96"  "Indices =  97"  "Indices =  98" 
##  [9] "Indices =  99"  "Indices =  100" "Indices =  101" "Indices =  102"
## [13] "Indices =  103" "Indices =  104" "Indices =  105"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 2.580796931" "Concs = 4.589962599" "Concs = 4.339108289"
##  [4] "Concs = 4.759629498" "Concs = 6.081131385" "Concs = 4.761075887"
##  [7] "Concs = 6.970865526" "Concs = 5.864292522" "Concs = 8.990170569"
## [10] "Concs = 10.29254833" "Concs = 11.89986315" "Concs = 10.55439287"
## [13] "Concs = 12.66145718" "Concs = 13.84087365" "Concs = 12.77355717"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      3.9025       0.1067  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.32170 -0.74272 -0.01223  0.50734  1.88653 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 3.902497   0.403600   9.669 2.65e-07 ***
## Time[ind]   0.106705   0.007969  13.390 5.55e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9972 on 13 degrees of freedom
## Multiple R-squared:  0.9324, Adjusted R-squared:  0.9272 
## F-statistic: 179.3 on 1 and 13 DF,  p-value: 5.555e-09

## (Intercept)   Time[ind] 
##   3.9024967   0.1067047 
##                  2.5 %    97.5 %
## (Intercept) 3.03057157 4.7744218
## Time[ind]   0.08948862 0.1239209
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  106" "Indices =  107" "Indices =  108" "Indices =  109"
##  [5] "Indices =  110" "Indices =  111" "Indices =  112" "Indices =  113"
##  [9] "Indices =  114" "Indices =  115" "Indices =  116" "Indices =  117"
## [13] "Indices =  118" "Indices =  119" "Indices =  120"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 4.642200138" "Concs = 4.107381982" "Concs = 3.642209544"
##  [4] "Concs = 6.090475637" "Concs = 5.80525893"  "Concs = 8.98551562" 
##  [7] "Concs = 6.941039356" "Concs = 7.206821805" "Concs = 10.94796175"
## [10] "Concs = 13.80091931" "Concs = 7.457397291" "Concs = 9.668427529"
## [13] "Concs = 16.81467648" "Concs = 18.96446187" "Concs = 16.539466"  
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      4.1926       0.1346  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.8096 -0.7867 -0.0852  1.0222  2.7743 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   4.1926     0.8557   4.900  0.00029 ***
## Time[ind]     0.1346     0.0169   7.965 2.35e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.114 on 13 degrees of freedom
## Multiple R-squared:  0.8299, Adjusted R-squared:  0.8169 
## F-statistic: 63.44 on 1 and 13 DF,  p-value: 2.346e-06

## (Intercept)   Time[ind] 
##   4.1925881   0.1345733 
##                  2.5 %    97.5 %
## (Intercept) 2.34396600 6.0412103
## Time[ind]   0.09807234 0.1710743
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  121" "Indices =  122" "Indices =  123" "Indices =  124"
##  [5] "Indices =  125" "Indices =  126" "Indices =  127" "Indices =  128"
##  [9] "Indices =  129" "Indices =  130" "Indices =  131"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 30"
##  [6] "Times = 30" "Times = 60" "Times = 60" "Times = 60" "Times = 90"
## [11] "Times = 90"
##  [1] "Concs = 19.16500098" "Concs = 25.91267967" "Concs = 22.19280552"
##  [4] "Concs = 17.62020275" "Concs = 24.15778887" "Concs = 20.49970666"
##  [7] "Concs = 25.33183553" "Concs = 23.63873667" "Concs = 25.85088774"
## [10] "Concs = 28.34728168" "Concs = 25.77673742"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    20.77252      0.06666  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.1522 -1.3704  0.4204  1.2322  5.1402 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 20.77252    1.27599  16.279 5.53e-08 ***
## Time[ind]    0.06666    0.02474   2.694   0.0246 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.576 on 9 degrees of freedom
## Multiple R-squared:  0.4464, Adjusted R-squared:  0.3849 
## F-statistic: 7.257 on 1 and 9 DF,  p-value: 0.02464

## (Intercept)   Time[ind] 
## 20.77252385  0.06665756 
##                   2.5 %    97.5 %
## (Intercept) 17.88602380 23.659024
## Time[ind]    0.01068116  0.122634
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  0.68 10 2.89 50 75 100 125 150 250
##  $ vel: num  -15.7 53.4 19.5 234.4 273.9 ...
##      sub       vel
## 1   0.68 -15.74820
## 2  10.00  53.42394
## 3   2.89  19.54617
## 4  50.00 234.39964
## 5  75.00 273.89275
## 6 100.00 434.88717
## 7 125.00 533.52372
## 8 150.00 672.86659
## 9 250.00 333.28779

fipronil

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 105.7355056" "Concs = 71.31297707" "Concs = 79.81665852"
##  [4] "Concs = 7.601993848" "Concs = 11.87171779" "Concs = 8.347482218"
##  [7] "Concs = 12.54233702" "Concs = 9.213313367" "Concs = 10.38856477"
## [10] "Concs = 12.36949156" "Concs = 8.215365646" "Concs = 11.17931895"
## [13] "Concs = 12.71923746" "Concs = 9.99477721" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     50.9177      -0.5992  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -34.328 -22.896  -3.587  15.344  54.818 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  50.9177    11.4177   4.460  0.00078 ***
## Time[ind]    -0.5992     0.2184  -2.743  0.01783 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 26.79 on 12 degrees of freedom
## Multiple R-squared:  0.3854, Adjusted R-squared:  0.3342 
## F-statistic: 7.525 on 1 and 12 DF,  p-value: 0.01783

## (Intercept)   Time[ind] 
##  50.9177421  -0.5991924 
##                 2.5 %     97.5 %
## (Intercept) 26.040763 75.7947212
## Time[ind]   -1.075125 -0.1232592
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  15" "Indices =  16" "Indices =  17" "Indices =  18"
##  [5] "Indices =  19" "Indices =  20" "Indices =  21" "Indices =  22"
##  [9] "Indices =  23" "Indices =  24" "Indices =  25" "Indices =  26"
## [13] "Indices =  27" "Indices =  28" "Indices =  29"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 3.553166435" "Concs = 2.185797914" "Concs = 4.160901096"
##  [4] "Concs = 0.961731316" "Concs = 0.608701865" "Concs = 2.021395291"
##  [7] "Concs = 0.34095865"  "Concs = 1.416552854" "Concs = 4.678731136"
## [10] "Concs = 1.597568113" "Concs = 2.059112975" "Concs = 4.336224939"
## [13] "Concs = 0.73593197"  "Concs = 1.01143428"  "Concs = 2.098949857"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     2.53175     -0.01061  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8724 -0.8187 -0.3459  0.7719  2.4654 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.53175    0.57930   4.370 0.000758 ***
## Time[ind]   -0.01061    0.01144  -0.928 0.370357    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.431 on 13 degrees of freedom
## Multiple R-squared:  0.06212,    Adjusted R-squared:  -0.01003 
## F-statistic: 0.861 on 1 and 13 DF,  p-value: 0.3704

## (Intercept)   Time[ind] 
##  2.53174769 -0.01061377 
##                   2.5 %     97.5 %
## (Intercept)  1.28025077 3.78324461
## Time[ind]   -0.03532453 0.01409699
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  30" "Indices =  31" "Indices =  32" "Indices =  33"
##  [5] "Indices =  34" "Indices =  35" "Indices =  36" "Indices =  37"
##  [9] "Indices =  38" "Indices =  39" "Indices =  40" "Indices =  41"
## [13] "Indices =  42" "Indices =  43" "Indices =  44"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 285.0383486" "Concs = 295.6872209" "Concs = 261.2375276"
##  [4] "Concs = 223.3849191" "Concs = 19.09530124" "Concs = 61.85004879"
##  [7] "Concs = 76.72890033" "Concs = 65.4447593"  "Concs = 59.88633813"
## [10] "Concs = 74.09066447" "Concs = 65.54242812" "Concs = 39.55208359"
## [13] "Concs = 66.15498564" "Concs = 23.55175796" "Concs = 58.25965938"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     188.031       -1.957  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -139.578  -58.228    3.492   59.492  107.656 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 188.0314    31.2086   6.025 4.27e-05 ***
## Time[ind]    -1.9572     0.6162  -3.176  0.00729 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 77.11 on 13 degrees of freedom
## Multiple R-squared:  0.4369, Adjusted R-squared:  0.3936 
## F-statistic: 10.09 on 1 and 13 DF,  p-value: 0.007294

## (Intercept)   Time[ind] 
##  188.031379   -1.957206 
##                  2.5 %      97.5 %
## (Intercept) 120.609359 255.4533982
## Time[ind]    -3.288452  -0.6259611
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  45" "Indices =  46" "Indices =  47" "Indices =  48"
##  [5] "Indices =  49" "Indices =  50" "Indices =  51" "Indices =  52"
##  [9] "Indices =  53" "Indices =  54" "Indices =  55" "Indices =  56"
## [13] "Indices =  57" "Indices =  58"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 49.56034014" "Concs = 49.17468426" "Concs = 36.68866915"
##  [4] "Concs = 35.05455395" "Concs = 40.30349338" "Concs = 44.1381674" 
##  [7] "Concs = 38.08049817" "Concs = 38.34527612" "Concs = 89.31881211"
## [10] "Concs = 40.27279664" "Concs = 55.95173867" "Concs = 37.82415225"
## [13] "Concs = 32.32010713" "Concs = 45.93427684"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    47.06620     -0.04945  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -11.270  -7.436  -4.309   2.398  43.736 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 47.06620    5.96482   7.891 4.33e-06 ***
## Time[ind]   -0.04945    0.11951  -0.414    0.686    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14.73 on 12 degrees of freedom
## Multiple R-squared:  0.01406,    Adjusted R-squared:  -0.0681 
## F-statistic: 0.1712 on 1 and 12 DF,  p-value: 0.6864

## (Intercept)   Time[ind] 
## 47.06619751 -0.04944609 
##                  2.5 %     97.5 %
## (Intercept) 34.0699795 60.0624155
## Time[ind]   -0.3098359  0.2109437
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  59" "Indices =  60" "Indices =  61" "Indices =  62"
##  [5] "Indices =  63" "Indices =  64" "Indices =  65" "Indices =  66"
##  [9] "Indices =  67" "Indices =  68" "Indices =  69" "Indices =  70"
## [13] "Indices =  71" "Indices =  72" "Indices =  73"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 32.55124669" "Concs = 72.28565415" "Concs = 50.30200713"
##  [4] "Concs = 65.75118371" "Concs = 61.03836189" "Concs = 86.42270417"
##  [7] "Concs = 18.77293974" "Concs = 84.04356305" "Concs = 89.30314297"
## [10] "Concs = 60.95565287" "Concs = 89.79580177" "Concs = 90.59062961"
## [13] "Concs = 56.03613412" "Concs = 94.58659729" "Concs = 89.70085579"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     58.4479       0.2828  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -48.158 -11.302   5.804  14.779  23.733 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  58.4479     8.8289   6.620 1.66e-05 ***
## Time[ind]     0.2828     0.1743   1.622    0.129    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 21.82 on 13 degrees of freedom
## Multiple R-squared:  0.1683, Adjusted R-squared:  0.1043 
## F-statistic: 2.631 on 1 and 13 DF,  p-value: 0.1288

## (Intercept)   Time[ind] 
##  58.4479335   0.2827649 
##                   2.5 %     97.5 %
## (Intercept) 39.37416273 77.5217042
## Time[ind]   -0.09384598  0.6593758
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  74" "Indices =  75" "Indices =  76" "Indices =  77"
##  [5] "Indices =  78" "Indices =  79" "Indices =  80" "Indices =  81"
##  [9] "Indices =  82" "Indices =  83" "Indices =  84" "Indices =  85"
## [13] "Indices =  86" "Indices =  87" "Indices =  88"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 58.45901219" "Concs = 51.85481179" "Concs = 53.89065136"
##  [4] "Concs = 62.24891641" "Concs = 54.68420677" "Concs = 91.10795719"
##  [7] "Concs = 51.66702524" "Concs = 65.6950903"  "Concs = 112.1237445"
## [10] "Concs = 62.81350539" "Concs = 74.14828799" "Concs = 93.87631612"
## [13] "Concs = 59.80299767" "Concs = 82.33654045" "Concs = 89.20514072"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     62.9985       0.2033  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -21.493 -11.254  -3.799   4.474  43.026 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  62.9985     7.2701   8.665 9.23e-07 ***
## Time[ind]     0.2033     0.1435   1.416     0.18    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.96 on 13 degrees of freedom
## Multiple R-squared:  0.1337, Adjusted R-squared:  0.06704 
## F-statistic: 2.006 on 1 and 13 DF,  p-value: 0.1802

## (Intercept)   Time[ind] 
##  62.9984959   0.2033107 
##                  2.5 %     97.5 %
## (Intercept) 47.2924980 78.7044939
## Time[ind]   -0.1068036  0.5134251
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  89"  "Indices =  90"  "Indices =  91"  "Indices =  92" 
##  [5] "Indices =  93"  "Indices =  94"  "Indices =  95"  "Indices =  96" 
##  [9] "Indices =  97"  "Indices =  98"  "Indices =  99"  "Indices =  100"
## [13] "Indices =  101" "Indices =  102" "Indices =  103"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 80.1226913"  "Concs = 96.90138648" "Concs = 94.88883577"
##  [4] "Concs = 37.15191594" "Concs = 76.95257401" "Concs = 82.83018255"
##  [7] "Concs = 89.28298886" "Concs = 103.9076465" "Concs = 88.89209516"
## [10] "Concs = 75.20034761" "Concs = 99.21349783" "Concs = 86.10641447"
## [13] "Concs = 85.35534061" "Concs = 86.89358929" "Concs = 19.45762438"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     86.7399      -0.1674  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -52.214  -4.056   7.566  11.922  22.519 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  86.7399     9.2758   9.351  3.9e-07 ***
## Time[ind]    -0.1674     0.1832  -0.914    0.377    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 22.92 on 13 degrees of freedom
## Multiple R-squared:  0.0604, Adjusted R-squared:  -0.01188 
## F-statistic: 0.8356 on 1 and 13 DF,  p-value: 0.3773

## (Intercept)   Time[ind] 
##  86.7399137  -0.1674215 
##                  2.5 %      97.5 %
## (Intercept) 66.7007990 106.7790284
## Time[ind]   -0.5630931   0.2282501
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  104" "Indices =  105" "Indices =  106" "Indices =  107"
##  [5] "Indices =  108" "Indices =  109" "Indices =  110" "Indices =  111"
##  [9] "Indices =  112" "Indices =  113" "Indices =  114" "Indices =  115"
## [13] "Indices =  116" "Indices =  117" "Indices =  118"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 161.3373216" "Concs = 140.3753919" "Concs = 143.641415" 
##  [4] "Concs = 143.5820327" "Concs = 117.0381728" "Concs = 105.3992543"
##  [7] "Concs = 120.601107"  "Concs = 115.1379412" "Concs = 126.1830373"
## [10] "Concs = 91.91948648" "Concs = 106.6462813" "Concs = 72.50149496"
## [13] "Concs = 112.4063583" "Concs = 105.3992543" "Concs = 111.7531537"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    135.4719      -0.4413  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -36.493  -9.455   3.950  12.187  25.865 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 135.4719     7.0902  19.107 6.75e-11 ***
## Time[ind]    -0.4413     0.1400  -3.152  0.00764 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.52 on 13 degrees of freedom
## Multiple R-squared:  0.4332, Adjusted R-squared:  0.3896 
## F-statistic: 9.936 on 1 and 13 DF,  p-value: 0.00764

## (Intercept)   Time[ind] 
## 135.4719208  -0.4412942 
##                   2.5 %      97.5 %
## (Intercept) 120.1543894 150.7894522
## Time[ind]    -0.7437383  -0.1388501
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  119" "Indices =  120" "Indices =  121" "Indices =  122"
##  [5] "Indices =  123" "Indices =  124" "Indices =  125" "Indices =  126"
##  [9] "Indices =  127" "Indices =  128" "Indices =  129" "Indices =  130"
## [13] "Indices =  131" "Indices =  132" "Indices =  133"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 94.37993663" "Concs = 113.4786371" "Concs = 91.29136792"
##  [4] "Concs = 105.2844752" "Concs = 83.9166222"  "Concs = 57.25407999"
##  [7] "Concs = 71.31021926" "Concs = 93.93871253" "Concs = 36.95777127"
## [10] "Concs = 77.4873567"  "Concs = 101.3134582" "Concs = 91.54349597"
## [13] "Concs = 58.38865626" "Concs = 74.14665992" "Concs = 61.1620649" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     90.3680      -0.2456  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -46.043  -8.490   1.854  13.424  25.680 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  90.3680     8.1298   11.12  5.2e-08 ***
## Time[ind]    -0.2456     0.1605   -1.53     0.15    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.09 on 13 degrees of freedom
## Multiple R-squared:  0.1526, Adjusted R-squared:  0.08739 
## F-statistic: 2.341 on 1 and 13 DF,  p-value: 0.15

## (Intercept)   Time[ind] 
##  90.3679851  -0.2455834 
##                  2.5 %      97.5 %
## (Intercept) 72.8046674 107.9313029
## Time[ind]   -0.5923704   0.1012037
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  10 2.89 50 75 100 125 150 200 250
##  $ vel: num  2996 53.1 9786 247.2 -1413.8 ...
##      sub         vel
## 1  10.00  2995.96183
## 2   2.89    53.06886
## 3  50.00  9786.03192
## 4  75.00   247.23047
## 5 100.00 -1413.82455
## 6 125.00 -1016.55355
## 7 150.00   837.10748
## 8 200.00  2206.47101
## 9 250.00  1227.91678

fipsulf

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.125996797" "Concs = 0.047756822" "Concs = 0.057531836"
##  [4] "Concs = 0.226052779" "Concs = 0.249546426" "Concs = 0.249495111"
##  [7] "Concs = 0.556306401" "Concs = 0.629523416" "Concs = 0.545734442"
## [10] "Concs = 1.029532274" "Concs = 1.020828782" "Concs = 1.121529265"
## [13] "Concs = 1.478049545" "Concs = 1.552223152" "Concs = 1.605171177"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.04966      0.01667  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.073616 -0.039497 -0.001901  0.031662  0.079844 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0496582  0.0217059   2.288   0.0395 *  
## Time[ind]   0.0166674  0.0004286  38.889 7.71e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.05363 on 13 degrees of freedom
## Multiple R-squared:  0.9915, Adjusted R-squared:  0.9908 
## F-statistic:  1512 on 1 and 13 DF,  p-value: 7.707e-15

## (Intercept)   Time[ind] 
##  0.04965817  0.01666736 
##                   2.5 %     97.5 %
## (Intercept) 0.002765368 0.09655097
## Time[ind]   0.015741464 0.01759326
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [7] "Concs = 0.072417652" "Concs = 0.105189206" "Concs = 0.093830232"
## [10] "Concs = 0.446059868" "Concs = 0.501873862" "Concs = 1.937676963"
## [13] "Concs = 0.541481009" "Concs = 0.713021528" "Concs = 0.948269563"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    -0.06729      0.01089  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.37110 -0.15983 -0.09602  0.05149  1.35172 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) -0.067286   0.164967  -0.408   0.6900   
## Time[ind]    0.010887   0.003257   3.342   0.0053 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4076 on 13 degrees of freedom
## Multiple R-squared:  0.4622, Adjusted R-squared:  0.4208 
## F-statistic: 11.17 on 1 and 13 DF,  p-value: 0.005297

## (Intercept)   Time[ind] 
## -0.06728624  0.01088737 
##                    2.5 %     97.5 %
## (Intercept) -0.423675199 0.28910272
## Time[ind]    0.003850487 0.01792426
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 1.232923543" "Concs = 6.086978824" "Concs = 0.564979782"
##  [4] "Concs = 2.509901494" "Concs = 0.497072024" "Concs = 0.573048602"
##  [7] "Concs = 0.208702278" "Concs = 1.224307072" "Concs = 0.86186791" 
## [10] "Concs = 2.640613398" "Concs = 2.278728642" "Concs = 1.938091721"
## [13] "Concs = 3.288556396" "Concs = 2.79424236"  "Concs = 2.85277407" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     1.50788      0.01185  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.6548 -0.9723 -0.2750  0.3498  4.5791 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  1.50788    0.61796   2.440   0.0298 *
## Time[ind]    0.01185    0.01220   0.972   0.3490  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.527 on 13 degrees of freedom
## Multiple R-squared:  0.06769,    Adjusted R-squared:  -0.004025 
## F-statistic: 0.9439 on 1 and 13 DF,  p-value: 0.349

## (Intercept)   Time[ind] 
##  1.50787526  0.01185412 
##                   2.5 %     97.5 %
## (Intercept)  0.17286420 2.84288632
## Time[ind]   -0.01450563 0.03821386
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.61596018"  "Concs = 0.004496637" "Concs = 0.393574273"
##  [7] "Concs = 1.00896852"  "Concs = 1.080335369" "Concs = 1.122428808"
## [10] "Concs = 0.794034486" "Concs = 1.567175192" "Concs = 1.445091993"
## [13] "Concs = 1.567376573" "Concs = 1.397216044"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.19848      0.01565  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.4288 -0.1985 -0.1010  0.3013  0.4543 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.19848    0.12829   1.547    0.148    
## Time[ind]    0.01565    0.00257   6.090 5.42e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3168 on 12 degrees of freedom
## Multiple R-squared:  0.7555, Adjusted R-squared:  0.7351 
## F-statistic: 37.08 on 1 and 12 DF,  p-value: 5.421e-05

## (Intercept)   Time[ind] 
##  0.19848307  0.01565313 
##                   2.5 %     97.5 %
## (Intercept) -0.08104254 0.47800868
## Time[ind]    0.01005261 0.02125366
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  60" "Indices =  61" "Indices =  62" "Indices =  63"
##  [5] "Indices =  64" "Indices =  65" "Indices =  66" "Indices =  67"
##  [9] "Indices =  68" "Indices =  69" "Indices =  70" "Indices =  71"
## [13] "Indices =  72" "Indices =  73" "Indices =  74"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.064056262" "Concs = 0.084903651" "Concs = 0.054098343"
##  [4] "Concs = 1.037370756" "Concs = 1.004548869" "Concs = 1.211451943"
##  [7] "Concs = 1.770038982" "Concs = 1.964421756" "Concs = 2.082784287"
## [10] "Concs = 2.421230649" "Concs = 2.716290502" "Concs = 2.511880669"
## [13] "Concs = 2.884476336" "Concs = 3.658963096" "Concs = 3.101044324"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.49072      0.03283  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.56113 -0.37519  0.05124  0.24195  0.60710 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.490719   0.152077   3.227  0.00662 ** 
## Time[ind]   0.032832   0.003003  10.934 6.32e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3758 on 13 degrees of freedom
## Multiple R-squared:  0.9019, Adjusted R-squared:  0.8944 
## F-statistic: 119.6 on 1 and 13 DF,  p-value: 6.325e-08

## (Intercept)   Time[ind] 
##   0.4907187   0.0328321 
##                  2.5 %     97.5 %
## (Intercept) 0.16217637 0.81926107
## Time[ind]   0.02634505 0.03931916
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  75" "Indices =  76" "Indices =  77" "Indices =  78"
##  [5] "Indices =  79" "Indices =  80" "Indices =  81" "Indices =  82"
##  [9] "Indices =  83" "Indices =  84" "Indices =  85" "Indices =  86"
## [13] "Indices =  87" "Indices =  88" "Indices =  89"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 1.0685532"   "Concs = 1.193964217" "Concs = 1.061157254"
##  [7] "Concs = 1.739690158" "Concs = 1.568026457" "Concs = 1.831902381"
## [10] "Concs = 2.58185903"  "Concs = 2.518118409" "Concs = 2.706182414"
## [13] "Concs = 3.388713261" "Concs = 3.265199632" "Concs = 3.360717697"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.38590      0.03504  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.38590 -0.22611  0.09385  0.18765  0.39495 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.385901   0.113655   3.395  0.00478 ** 
## Time[ind]   0.035035   0.002244  15.612 8.42e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2808 on 13 degrees of freedom
## Multiple R-squared:  0.9494, Adjusted R-squared:  0.9455 
## F-statistic: 243.7 on 1 and 13 DF,  p-value: 8.42e-10

## (Intercept)   Time[ind] 
##  0.38590066  0.03503517 
##                  2.5 %     97.5 %
## (Intercept) 0.14036476 0.63143656
## Time[ind]   0.03018707 0.03988327
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  90"  "Indices =  91"  "Indices =  92"  "Indices =  93" 
##  [5] "Indices =  94"  "Indices =  95"  "Indices =  96"  "Indices =  97" 
##  [9] "Indices =  98"  "Indices =  99"  "Indices =  100" "Indices =  101"
## [13] "Indices =  102" "Indices =  103" "Indices =  104"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.319307475" "Concs = 0.322811871" "Concs = 0.334641014"
##  [4] "Concs = 1.513101462" "Concs = 1.254618226" "Concs = 1.316915121"
##  [7] "Concs = 1.847166036" "Concs = 2.06265471"  "Concs = 2.225655093"
## [10] "Concs = 3.029089226" "Concs = 2.818619179" "Concs = 2.892261352"
## [13] "Concs = 3.395108251" "Concs = 3.493680617" "Concs = 3.346621743"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.73091      0.03284  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.41160 -0.31522  0.09348  0.24045  0.50969 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.730906   0.131800   5.546 9.46e-05 ***
## Time[ind]   0.032835   0.002602  12.617 1.14e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3257 on 13 degrees of freedom
## Multiple R-squared:  0.9245, Adjusted R-squared:  0.9187 
## F-statistic: 159.2 on 1 and 13 DF,  p-value: 1.142e-08

## (Intercept)   Time[ind] 
##  0.73090589  0.03283532 
##                  2.5 %     97.5 %
## (Intercept) 0.44616859 1.01564319
## Time[ind]   0.02721319 0.03845745
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  105" "Indices =  106" "Indices =  107" "Indices =  108"
##  [5] "Indices =  109" "Indices =  110" "Indices =  111" "Indices =  112"
##  [9] "Indices =  113" "Indices =  114" "Indices =  115" "Indices =  116"
## [13] "Indices =  117" "Indices =  118" "Indices =  119"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0.139500206" "Concs = 0"          
##  [4] "Concs = 0.921840151" "Concs = 1.265455207" "Concs = 0.083794693"
##  [7] "Concs = 1.758009212" "Concs = 1.131761977" "Concs = 2.14032494" 
## [10] "Concs = 3.119569212" "Concs = 5.219960219" "Concs = 3.68483357" 
## [13] "Concs = 4.382618411" "Concs = 4.121095689" "Concs = 4.42249183" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      0.1508       0.0515  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.8396 -0.3835 -0.1214  0.2021  1.9790 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.150816   0.280672   0.537      0.6    
## Time[ind]   0.051503   0.005542   9.293 4.18e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6935 on 13 degrees of freedom
## Multiple R-squared:  0.8692, Adjusted R-squared:  0.8591 
## F-statistic: 86.37 on 1 and 13 DF,  p-value: 4.182e-07

## (Intercept)   Time[ind] 
##  0.15081593  0.05150259 
##                   2.5 %     97.5 %
## (Intercept) -0.45553864 0.75717051
## Time[ind]    0.03953014 0.06347504
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  120" "Indices =  121" "Indices =  122" "Indices =  123"
##  [5] "Indices =  124" "Indices =  125" "Indices =  126" "Indices =  127"
##  [9] "Indices =  128" "Indices =  129" "Indices =  130" "Indices =  131"
## [13] "Indices =  132" "Indices =  133" "Indices =  134"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.688691412" "Concs = 0.680203691" "Concs = 0.671715969"
##  [7] "Concs = 1.128032043" "Concs = 1.057705208" "Concs = 1.0791266"  
## [10] "Concs = 1.670842039" "Concs = 1.655483305" "Concs = 1.672054571"
## [13] "Concs = 2.11584115"  "Concs = 2.394723427" "Concs = 2.276703681"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      0.2111       0.0238  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.23753 -0.14388  0.03278  0.11632  0.20285 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.211083   0.063521   3.323   0.0055 ** 
## Time[ind]   0.023803   0.001254  18.978 7.35e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.157 on 13 degrees of freedom
## Multiple R-squared:  0.9652, Adjusted R-squared:  0.9625 
## F-statistic: 360.2 on 1 and 13 DF,  p-value: 7.353e-11

## (Intercept)   Time[ind] 
##  0.21108314  0.02380321 
##                  2.5 %     97.5 %
## (Intercept) 0.07385384 0.34831244
## Time[ind]   0.02109362 0.02651279
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  10 2.89 50 75 100 125 150 200 250
##  $ vel: num  83.3 54.4 59.3 78.3 164.2 ...
##      sub       vel
## 1  10.00  83.33680
## 2   2.89  54.43687
## 3  50.00  59.27059
## 4  75.00  78.26567
## 5 100.00 164.16051
## 6 125.00 175.17585
## 7 150.00 164.17661
## 8 200.00 257.51296
## 9 250.00 119.01603

exposure experiment analysis

Results presentation and discussion for parent analytes (atrazine, triadimenon, and fipronil) and their xenobiotic metabolites.

Toxicity of parents and metabolites discussion.

Microsomal analysis of soil and amphibian data for 0 (soil only), 2, 4, 12, 24, and 48 hours after exposure.

Database has factors for time, parent (mapped to analyte), analyte (can be either parent or metabolite), matrix (amphibian or soil), and tank (potentially a nuisance variable).

## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame':  352 obs. of  6 variables:
##  $ time     : int  2 2 2 2 4 4 4 4 12 12 ...
##  $ parent   : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte  : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix   : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 1 1 1 1 1 ...
##  $ conc     : num  3.07 3.69 4.7 1.89 7.62 ...
##  $ replicate: Factor w/ 4 levels "1","2","3","4": 1 2 3 4 1 2 3 4 1 2 ...
##  - attr(*, "vars")=List of 4
##   ..$ : symbol parent
##   ..$ : symbol analyte
##   ..$ : symbol matrix
##   ..$ : symbol time
##  - attr(*, "drop")= logi TRUE
##  - attr(*, "indices")=List of 86
##   ..$ : int  0 1 2 3
##   ..$ : int  4 5 6 7
##   ..$ : int  8 9 10 11
##   ..$ : int  12 13 14 15
##   ..$ : int  16 17 18 19
##   ..$ : int  20 21 22 23
##   ..$ : int  24 25 26 27
##   ..$ : int  28 29 30 31
##   ..$ : int  32 33 34 35
##   ..$ : int  36 37 38 39
##   ..$ : int  40 41 42 43
##   ..$ : int  88 89 90 91
##   ..$ : int  92 93 94 95
##   ..$ : int  96 97 98 99
##   ..$ : int  100 101 102 103
##   ..$ : int  104 105 106 107
##   ..$ : int  108 109 110 111
##   ..$ : int  112 113 114 115
##   ..$ : int  116 117 118 119
##   ..$ : int  120 121 122 123
##   ..$ : int  124 125 126 127
##   ..$ : int  128 129 130 131
##   ..$ : int  44 45 46 47
##   ..$ : int  48 49 50 51
##   ..$ : int  52 53 54 55
##   ..$ : int  56 57 58 59
##   ..$ : int  60 61 62 63
##   ..$ : int  64 65 66 67
##   ..$ : int  68 69 70 71
##   ..$ : int  72 73 74 75
##   ..$ : int  76 77 78 79
##   ..$ : int  80 81 82 83
##   ..$ : int  84 85 86 87
##   ..$ : int  264 265 266 267
##   ..$ : int  268 269 270 271
##   ..$ : int  272 273 274 275
##   ..$ : int  276 277 278 279
##   ..$ : int  280 281 282 283
##   ..$ : int  284 285 286 287 288 289 290 291
##   ..$ : int  292 293 294 295
##   ..$ : int  296 297 298 299
##   ..$ : int  300 301 302 303
##   ..$ : int  304 305 306 307
##   ..$ : int  308 309 310 311
##   ..$ : int  312 313 314 315
##   ..$ : int  316 317 318 319
##   ..$ : int  320 321 322 323
##   ..$ : int  324 325 326 327
##   ..$ : int  328 329 330 331 332 333 334 335
##   ..$ : int  336 337 338 339
##   ..$ : int  340 341 342 343
##   ..$ : int  344 345 346 347
##   ..$ : int  348 349 350 351
##   ..$ : int  176 177 178 179
##   ..$ : int  180 181 182 183
##   ..$ : int  184 185 186 187
##   ..$ : int  188 189 190 191
##   ..$ : int  192 193 194 195
##   ..$ : int  196 197 198 199
##   ..$ : int  200 201 202 203
##   ..$ : int  204 205 206 207
##   ..$ : int  208 209 210 211
##   ..$ : int  212 213 214 215
##   ..$ : int  216 217 218 219
##   ..$ : int  220 221 222 223
##   ..$ : int  224 225 226 227
##   ..$ : int  228 229 230 231
##   ..$ : int  232 233 234 235
##   ..$ : int  236 237 238 239
##   ..$ : int  240 241 242 243
##   ..$ : int  244 245 246 247
##   ..$ : int  248 249 250 251
##   ..$ : int  252 253 254 255
##   ..$ : int  256 257 258 259
##   ..$ : int  260 261 262 263
##   ..$ : int  132 133 134 135
##   ..$ : int  136 137 138 139
##   ..$ : int  140 141 142 143
##   ..$ : int  144 145 146 147
##   ..$ : int  148 149 150 151
##   ..$ : int  152 153 154 155
##   ..$ : int  156 157 158 159
##   ..$ : int  160 161 162 163
##   ..$ : int  164 165 166 167
##   ..$ : int  168 169 170 171
##   ..$ : int  172 173 174 175
##  - attr(*, "group_sizes")= int  4 4 4 4 4 4 4 4 4 4 ...
##  - attr(*, "biggest_group_size")= int 8
##  - attr(*, "labels")='data.frame':   86 obs. of  4 variables:
##   ..$ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ analyte: Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 2 2 2 2 2 ...
##   ..$ time   : int  2 4 12 24 48 0 2 4 12 24 ...
##   ..- attr(*, "vars")=List of 4
##   .. ..$ : symbol parent
##   .. ..$ : symbol analyte
##   .. ..$ : symbol matrix
##   .. ..$ : symbol time
##   ..- attr(*, "drop")= logi TRUE
## Source: local data frame [352 x 6]
## Groups: parent, analyte, matrix, time [86]
## 
##     time   parent  analyte matrix     conc replicate
##    (int)   (fctr)   (fctr) (fctr)    (dbl)    (fctr)
## 1      2 atrazine atrazine amphib 3.068203         1
## 2      2 atrazine atrazine amphib 3.689640         2
## 3      2 atrazine atrazine amphib 4.701166         3
## 4      2 atrazine atrazine amphib 1.892494         4
## 5      4 atrazine atrazine amphib 7.624610         1
## 6      4 atrazine atrazine amphib 4.134300         2
## 7      4 atrazine atrazine amphib 2.050779         3
## 8      4 atrazine atrazine amphib 7.626486         4
## 9     12 atrazine atrazine amphib 2.452278         1
## 10    12 atrazine atrazine amphib 3.786893         2
## ..   ...      ...      ...    ...      ...       ...
## Source: local data frame [86 x 7]
## Groups: parent, analyte, matrix [?]
## 
##      parent  analyte matrix  time count  ConcMean    ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)     (dbl)     (dbl)
## 1  atrazine atrazine amphib     2     4  3.337876 1.1753225
## 2  atrazine atrazine amphib     4     4  5.359044 2.7518903
## 3  atrazine atrazine amphib    12     4  3.123811 1.2566289
## 4  atrazine atrazine amphib    24     4  1.554919 0.6096102
## 5  atrazine atrazine amphib    48     4  1.001887 0.3545473
## 6  atrazine atrazine   soil     0     4 15.930920 2.5911041
## 7  atrazine atrazine   soil     2     4 19.029034 4.3534303
## 8  atrazine atrazine   soil     4     4 18.770091 2.6953158
## 9  atrazine atrazine   soil    12     4 20.614190 3.8918511
## 10 atrazine atrazine   soil    24     4 24.996196 4.4473828
## ..      ...      ...    ...   ...   ...       ...       ...
## <!-- html table generated in R 3.2.3 by xtable 1.8-0 package -->
## <!-- Mon Feb 01 14:35:15 2016 -->
## <table border=1>
## <tr> <th>  </th> <th> parent </th> <th> analyte </th> <th> matrix </th> <th> time </th> <th> count </th> <th> ConcMean </th> <th> ConcSD </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 3.34 </td> <td align="right"> 1.18 </td> </tr>
##   <tr> <td align="right"> 2 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 5.36 </td> <td align="right"> 2.75 </td> </tr>
##   <tr> <td align="right"> 3 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 3.12 </td> <td align="right"> 1.26 </td> </tr>
##   <tr> <td align="right"> 4 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 1.55 </td> <td align="right"> 0.61 </td> </tr>
##   <tr> <td align="right"> 5 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 1.00 </td> <td align="right"> 0.35 </td> </tr>
##   <tr> <td align="right"> 6 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 15.93 </td> <td align="right"> 2.59 </td> </tr>
##   <tr> <td align="right"> 7 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 19.03 </td> <td align="right"> 4.35 </td> </tr>
##   <tr> <td align="right"> 8 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 18.77 </td> <td align="right"> 2.70 </td> </tr>
##   <tr> <td align="right"> 9 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 20.61 </td> <td align="right"> 3.89 </td> </tr>
##   <tr> <td align="right"> 10 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 25.00 </td> <td align="right"> 4.45 </td> </tr>
##   <tr> <td align="right"> 11 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 26.43 </td> <td align="right"> 4.38 </td> </tr>
##   <tr> <td align="right"> 12 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 13 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.03 </td> </tr>
##   <tr> <td align="right"> 14 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.05 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 15 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 16 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 17 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 18 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 19 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 20 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 21 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 22 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 23 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.33 </td> <td align="right"> 0.12 </td> </tr>
##   <tr> <td align="right"> 24 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.94 </td> <td align="right"> 0.76 </td> </tr>
##   <tr> <td align="right"> 25 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 1.08 </td> <td align="right"> 0.51 </td> </tr>
##   <tr> <td align="right"> 26 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 1.99 </td> <td align="right"> 1.35 </td> </tr>
##   <tr> <td align="right"> 27 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.66 </td> <td align="right"> 0.53 </td> </tr>
##   <tr> <td align="right"> 28 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 29 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> -0.01 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 30 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 31 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.07 </td> </tr>
##   <tr> <td align="right"> 32 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.03 </td> </tr>
##   <tr> <td align="right"> 33 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.06 </td> <td align="right"> 0.06 </td> </tr>
##   <tr> <td align="right"> 34 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 1.87 </td> <td align="right"> 1.35 </td> </tr>
##   <tr> <td align="right"> 35 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 1.30 </td> <td align="right"> 0.52 </td> </tr>
##   <tr> <td align="right"> 36 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.57 </td> <td align="right"> 0.24 </td> </tr>
##   <tr> <td align="right"> 37 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.27 </td> <td align="right"> 0.05 </td> </tr>
##   <tr> <td align="right"> 38 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.21 </td> <td align="right"> 0.13 </td> </tr>
##   <tr> <td align="right"> 39 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   8 </td> <td align="right"> 0.41 </td> <td align="right"> 0.45 </td> </tr>
##   <tr> <td align="right"> 40 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.87 </td> <td align="right"> 0.24 </td> </tr>
##   <tr> <td align="right"> 41 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.82 </td> <td align="right"> 0.17 </td> </tr>
##   <tr> <td align="right"> 42 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.70 </td> <td align="right"> 0.11 </td> </tr>
##   <tr> <td align="right"> 43 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.36 </td> <td align="right"> 0.06 </td> </tr>
##   <tr> <td align="right"> 44 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.35 </td> <td align="right"> 0.29 </td> </tr>
##   <tr> <td align="right"> 45 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.40 </td> <td align="right"> 0.48 </td> </tr>
##   <tr> <td align="right"> 46 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.61 </td> <td align="right"> 0.57 </td> </tr>
##   <tr> <td align="right"> 47 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 1.25 </td> <td align="right"> 0.53 </td> </tr>
##   <tr> <td align="right"> 48 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.91 </td> <td align="right"> 0.57 </td> </tr>
##   <tr> <td align="right"> 49 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   8 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 50 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 51 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 52 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 53 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 54 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.06 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 55 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.05 </td> </tr>
##   <tr> <td align="right"> 56 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 57 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 58 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 59 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 60 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 61 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 62 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 63 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 64 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 65 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 66 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.13 </td> <td align="right"> 0.05 </td> </tr>
##   <tr> <td align="right"> 67 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.05 </td> </tr>
##   <tr> <td align="right"> 68 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 69 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.03 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 70 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 71 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 72 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 73 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 74 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 75 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 76 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.39 </td> <td align="right"> 0.08 </td> </tr>
##   <tr> <td align="right"> 77 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.55 </td> <td align="right"> 0.30 </td> </tr>
##   <tr> <td align="right"> 78 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.75 </td> <td align="right"> 0.32 </td> </tr>
##   <tr> <td align="right"> 79 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.87 </td> <td align="right"> 0.86 </td> </tr>
##   <tr> <td align="right"> 80 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.25 </td> <td align="right"> 0.08 </td> </tr>
##   <tr> <td align="right"> 81 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 3.11 </td> <td align="right"> 0.85 </td> </tr>
##   <tr> <td align="right"> 82 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 3.66 </td> <td align="right"> 1.34 </td> </tr>
##   <tr> <td align="right"> 83 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 5.28 </td> <td align="right"> 0.37 </td> </tr>
##   <tr> <td align="right"> 84 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 5.93 </td> <td align="right"> 1.00 </td> </tr>
##   <tr> <td align="right"> 85 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 4.82 </td> <td align="right"> 0.32 </td> </tr>
##   <tr> <td align="right"> 86 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 4.18 </td> <td align="right"> 0.44 </td> </tr>
##    </table>

The amphibian data set summary statistics. Atrazine peaks at 4 hours and then declines monotonically. DEA peaks at 12 hours and DIA at 24. Fipronil steadily declines from its first observation at 2 hours with fipronil sulfone not peaking until 24 hours. Triadimenon peaks at 24 hours with its metabolites tdla and tdlb peaking at 4 hours.

## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame':  86 obs. of  7 variables:
##  $ parent  : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix  : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 2 2 2 2 2 ...
##  $ time    : int  2 4 12 24 48 0 2 4 12 24 ...
##  $ count   : int  4 4 4 4 4 4 4 4 4 4 ...
##  $ ConcMean: num  3.34 5.36 3.12 1.55 1 ...
##  $ ConcSD  : num  1.175 2.752 1.257 0.61 0.355 ...
##  - attr(*, "vars")=List of 3
##   ..$ : symbol parent
##   ..$ : symbol analyte
##   ..$ : symbol matrix
##  - attr(*, "drop")= logi TRUE
## Source: local data frame [6 x 7]
## Groups: parent, analyte, matrix [2]
## 
##     parent  analyte matrix  time count   ConcMean     ConcSD
##     (fctr)   (fctr) (fctr) (int) (int)      (dbl)      (dbl)
## 1 atrazine atrazine amphib     2     4 3.33787563 1.17532253
## 2 atrazine atrazine amphib     4     4 5.35904387 2.75189034
## 3 atrazine atrazine amphib    12     4 3.12381130 1.25662887
## 4 atrazine atrazine amphib    24     4 1.55491895 0.60961016
## 5 atrazine atrazine amphib    48     4 1.00188749 0.35454734
## 6 atrazine      dea amphib     2     4 0.01389877 0.00522407
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
## 
##      parent  analyte matrix  time count   ConcMean     ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)      (dbl)      (dbl)
## 1  atrazine atrazine amphib     2     4 3.33787563 1.17532253
## 2  atrazine atrazine amphib     4     4 5.35904387 2.75189034
## 3  atrazine atrazine amphib    12     4 3.12381130 1.25662887
## 4  atrazine atrazine amphib    24     4 1.55491895 0.60961016
## 5  atrazine atrazine amphib    48     4 1.00188749 0.35454734
## 6  atrazine      dea amphib     2     4 0.01389877 0.00522407
## 7  atrazine      dea amphib     4     4 0.04436711 0.02843181
## 8  atrazine      dea amphib    12     4 0.05402182 0.01282235
## 9  atrazine      dea amphib    24     4 0.03652473 0.01310278
## 10 atrazine      dea amphib    48     4 0.01951501 0.01958540
## 11 atrazine      dia amphib     2     4 0.32878185 0.12495746
## 12 atrazine      dia amphib     4     4 0.94192818 0.76074427
## 13 atrazine      dia amphib    12     4 1.08350960 0.50576827
## 14 atrazine      dia amphib    24     4 1.98835970 1.34925248
## 15 atrazine      dia amphib    48     4 0.66238821 0.53051448
## [1] "atrazine"
## [1] "dea"
## [1] "dia"
## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
## 
##      parent  analyte matrix  time count  ConcMean     ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)     (dbl)      (dbl)
## 1  fipronil fipronil amphib     2     4 1.8670398 1.34631230
## 2  fipronil fipronil amphib     4     4 1.3005836 0.52188454
## 3  fipronil fipronil amphib    12     4 0.5659565 0.24026633
## 4  fipronil fipronil amphib    24     4 0.2676732 0.05106111
## 5  fipronil fipronil amphib    48     4 0.2119504 0.13140536
## 6  fipronil  fipsulf amphib     2     4 0.3465734 0.28711156
## 7  fipronil  fipsulf amphib     4     4 0.3966089 0.47739157
## 8  fipronil  fipsulf amphib    12     4 0.6129114 0.57346517
## 9  fipronil  fipsulf amphib    24     4 1.2528179 0.52648677
## 10 fipronil  fipsulf amphib    48     4 0.9067126 0.56596417
## Source: local data frame [0 x 7]
## Groups: parent, analyte, matrix [0]
## 
## Variables not shown: parent (fctr), analyte (fctr), matrix (fctr), time
##   (int), count (int), ConcMean (dbl), ConcSD (dbl)

The soil data set summary statistics. Atrazine in soil showing an upwards trend (need to test if significant) with dia and dea levels very low indicating little degradation in soil over the 48 hour period. Fipronil and triadimenon data also indicating little degradation in soil.

## Source: local data frame [18 x 7]
## Groups: parent, analyte, matrix [3]
## 
##      parent  analyte matrix  time count     ConcMean      ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)        (dbl)       (dbl)
## 1  atrazine atrazine   soil     0     4 15.930919692 2.591104068
## 2  atrazine atrazine   soil     2     4 19.029034412 4.353430337
## 3  atrazine atrazine   soil     4     4 18.770091080 2.695315758
## 4  atrazine atrazine   soil    12     4 20.614190363 3.891851074
## 5  atrazine atrazine   soil    24     4 24.996195532 4.447382801
## 6  atrazine atrazine   soil    48     4 26.434744900 4.377099498
## 7  atrazine      dea   soil     0     4  0.000000000 0.000000000
## 8  atrazine      dea   soil     2     4  0.001570429 0.000633009
## 9  atrazine      dea   soil     4     4  0.002999216 0.001537652
## 10 atrazine      dea   soil    12     4  0.005469015 0.004234880
## 11 atrazine      dea   soil    24     4  0.007308439 0.001736211
## 12 atrazine      dea   soil    48     4  0.008784632 0.003772339
## 13 atrazine      dia   soil     0     4  0.000000000 0.000000000
## 14 atrazine      dia   soil     2     4 -0.007727286 0.007374085
## 15 atrazine      dia   soil     4     4  0.020538600 0.020166308
## 16 atrazine      dia   soil    12     4  0.077036921 0.067772652
## 17 atrazine      dia   soil    24     4  0.042975804 0.030007793
## 18 atrazine      dia   soil    48     4  0.063693292 0.058241606
## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
## 
##      parent  analyte matrix  time count   ConcMean      ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)      (dbl)       (dbl)
## 1  fipronil fipronil   soil     2     8 0.40768123 0.447265792
## 2  fipronil fipronil   soil     4     4 0.86826316 0.244191727
## 3  fipronil fipronil   soil    12     4 0.81738069 0.169691335
## 4  fipronil fipronil   soil    24     4 0.70225877 0.108745058
## 5  fipronil fipronil   soil    48     4 0.35560948 0.058543752
## 6  fipronil  fipsulf   soil     2     8 0.01022479 0.012898421
## 7  fipronil  fipsulf   soil     4     4 0.02193831 0.010765665
## 8  fipronil  fipsulf   soil    12     4 0.01829893 0.005013814
## 9  fipronil  fipsulf   soil    24     4 0.01917848 0.009139211
## 10 fipronil  fipsulf   soil    48     4 0.01262887 0.005517408
## Source: local data frame [0 x 7]
## Groups: parent, analyte, matrix [0]
## 
## Variables not shown: parent (fctr), analyte (fctr), matrix (fctr), time
##   (int), count (int), ConcMean (dbl), ConcSD (dbl)
pdf(paste(micro.graphics,"data_mean_scatterplot",".pdf", sep=""))
  par(mfrow=c(3,1))
  print(parents)
## [1] atrazine    triadimefon fipronil   
## Levels: atrazine fipronil triadimefon
  for(parent in parents){
    i=0
    print(parent)
    temp.parent <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
    print(temp.parent)
    parent.analytes <- unique(temp.parent$analyte)
    for(analyte in parent.analytes){
      print(parent)
      print(analyte) 
      analytetemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$analyte==analyte),]
      xvalues <- as.numeric(as.character(analytetemp$time))
      points.y <- micro.amphib[which(micro.amphib$analyte==analyte),]$conc
      points.x <- as.numeric(as.character(micro.amphib[which(micro.amphib$analyte==analyte),]$time))
      #create empty plot if needed
      if(i==0){
        parenttemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
        maxconc <- max(points.y) 
        plot(xvalues,analytetemp$ConcMean,type="l", xlim=c(0,48),
             ylim = c(0,maxconc), main=parent,col="black", xlab="Hours", ylab="Concentration")
        axis(1,at=xvalues)
        i=1
      }
      #add line for parent metabolite
      if(analyte %in% parents){
        lines(xvalues,analytetemp$ConcMean,type="l",col="red")
        points(points.x, points.y, col = "red")
      }else{
      #add line for daughter metabolite
        lines(xvalues,analytetemp$ConcMean,type="l",col="blue")
        points(points.x, points.y, col = "blue")
      }
    }
  }
## [1] "atrazine"
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
## 
##      parent  analyte matrix  time count   ConcMean     ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)      (dbl)      (dbl)
## 1  atrazine atrazine amphib     2     4 3.33787563 1.17532253
## 2  atrazine atrazine amphib     4     4 5.35904387 2.75189034
## 3  atrazine atrazine amphib    12     4 3.12381130 1.25662887
## 4  atrazine atrazine amphib    24     4 1.55491895 0.60961016
## 5  atrazine atrazine amphib    48     4 1.00188749 0.35454734
## 6  atrazine      dea amphib     2     4 0.01389877 0.00522407
## 7  atrazine      dea amphib     4     4 0.04436711 0.02843181
## 8  atrazine      dea amphib    12     4 0.05402182 0.01282235
## 9  atrazine      dea amphib    24     4 0.03652473 0.01310278
## 10 atrazine      dea amphib    48     4 0.01951501 0.01958540
## 11 atrazine      dia amphib     2     4 0.32878185 0.12495746
## 12 atrazine      dia amphib     4     4 0.94192818 0.76074427
## 13 atrazine      dia amphib    12     4 1.08350960 0.50576827
## 14 atrazine      dia amphib    24     4 1.98835970 1.34925248
## 15 atrazine      dia amphib    48     4 0.66238821 0.53051448
## [1] "atrazine"
## [1] "atrazine"
## [1] "atrazine"
## [1] "dea"
## [1] "atrazine"
## [1] "dia"
## [1] "triadimefon"
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
## 
##         parent     analyte matrix  time count   ConcMean      ConcSD
##         (fctr)      (fctr) (fctr) (int) (int)      (dbl)       (dbl)
## 1  triadimefon        tdla amphib     2     4 0.05514470 0.021089764
## 2  triadimefon        tdla amphib     4     4 0.08150175 0.046221502
## 3  triadimefon        tdla amphib    12     4 0.03632384 0.015222899
## 4  triadimefon        tdla amphib    24     4 0.02400790 0.007522554
## 5  triadimefon        tdla amphib    48     4 0.01549908 0.004845715
## 6  triadimefon        tdlb amphib     2     4 0.08362714 0.016364595
## 7  triadimefon        tdlb amphib     4     4 0.13009543 0.054315693
## 8  triadimefon        tdlb amphib    12     4 0.07664673 0.048553355
## 9  triadimefon        tdlb amphib    24     4 0.04183235 0.011652266
## 10 triadimefon        tdlb amphib    48     4 0.02950214 0.003438978
## 11 triadimefon triadimefon amphib     2     4 0.38678831 0.075852995
## 12 triadimefon triadimefon amphib     4     4 0.54862458 0.300394386
## 13 triadimefon triadimefon amphib    12     4 0.75491439 0.318237965
## 14 triadimefon triadimefon amphib    24     4 0.86540039 0.860421208
## 15 triadimefon triadimefon amphib    48     4 0.24868748 0.079848623
## [1] "triadimefon"
## [1] "tdla"
## [1] "triadimefon"
## [1] "tdlb"
## [1] "triadimefon"
## [1] "triadimefon"
## [1] "fipronil"
## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
## 
##      parent  analyte matrix  time count  ConcMean     ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)     (dbl)      (dbl)
## 1  fipronil fipronil amphib     2     4 1.8670398 1.34631230
## 2  fipronil fipronil amphib     4     4 1.3005836 0.52188454
## 3  fipronil fipronil amphib    12     4 0.5659565 0.24026633
## 4  fipronil fipronil amphib    24     4 0.2676732 0.05106111
## 5  fipronil fipronil amphib    48     4 0.2119504 0.13140536
## 6  fipronil  fipsulf amphib     2     4 0.3465734 0.28711156
## 7  fipronil  fipsulf amphib     4     4 0.3966089 0.47739157
## 8  fipronil  fipsulf amphib    12     4 0.6129114 0.57346517
## 9  fipronil  fipsulf amphib    24     4 1.2528179 0.52648677
## 10 fipronil  fipsulf amphib    48     4 0.9067126 0.56596417
## [1] "fipronil"
## [1] "fipronil"
## [1] "fipronil"
## [1] "fipsulf"
dev.off()
## png 
##   2

la de da

turn times series to zoo objects

estimate lambdas using maximum likelihood for each time series

library(maxLik)

MLexp <- function(times, data){

expLik <- function(param) { y <- data t <- times alpha1 <- param[1] lambda1 <- param[2]-1(alpha1-lambda1t) - y/(exp(alpha1-lambda1*t)) }

max.fit <- maxLik(expLik, start = c(1,1)) crit <- qt(.975, length(data)-2) max.intercept.CI <- c(summary(max.fit)\(est[1,1]-crit*summary(max.fit)\)est[1,2],summary(max.fit)\(est[1,1]+crit*summary(max.fit)\)est[1,2]) max.decayrate.CI <- c(-1summary(max.fit)\(est[2,1]-crit*summary(max.fit)\)est[2,2],-1summary(max.fit)\(est[2,1]+crit*summary(max.fit)\)est[2,2]) max.halflife.CI <- c(log(2)/max.decayrate.CI[2],log(2)/max.decayrate.CI[1])

paste(“MLE for Initial Concentration =”,max.fit\(est[1], "MLE for decay rate =", max.fit\)est[2], “MLE for half life =”, -log(.5)/max.fit$est[2])

temp.list <- list(max.fit\(est[1], max.fit\)est[2], -log(.5)/max.fit$est[2], max.intercept.CI, max.decayrate.CI, max.halflife.CI, vcov(max.fit) ) return(temp.list) }

MLexp.intercept <- function(times, data) { temp.fit <- MLexp(times,data) temp.fit[[1]] }

MLexp.decayrate <- function(times, data) { temp.fit <- MLexp(times,data) temp.fit[[2]] }

MLexp.halflife <- function(times,data) { temp.fit <- MLexp(times,data) temp.fit[[3]] }

MLexp.intercept.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[4]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }

MLexp.decayrate.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[5]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }

MLexp.halflife.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[6]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }

microsome experiment analysis

data in csv format

======= glinski_metabolites

tested hypotheses

things to do

install and load supporting libraries

##        nodename 
## "stp-air.local"
## [1] "R version 3.2.2 (2015-08-14)"
## 
## Attaching package: 'MASS'
## 
## The following object is masked from 'package:dplyr':
## 
##     select
## 
## 
## 'drc' has been loaded.
## 
## Please cite R and 'drc' if used for a publication,
## for references type 'citation()' and 'citation('drc')'.
## [1] "list of loaded packages: "
##  [1] "scatterplot3d" "ggplot2"       "drc"           "MASS"         
##  [5] "xtable"        "zoo"           "knitr"         "dplyr"        
##  [9] "rmarkdown"     "stats"         "graphics"      "grDevices"    
## [13] "utils"         "datasets"      "methods"       "base"

import experimental exposure and microsomal data

Load csv files with experimental data and microsome data sets. The beolw may return false but still be OK if rstudio does not have privileges to data directory (e.g., attached drive).

## [1] "Root directory location: /Users/puruckertom/git/glinski_metabolites/"
## [1] "check to see if R can access files OK: TRUE"

experimental exposure data structure

Check out structure of imported data sets.

str(micro)
## 'data.frame':    352 obs. of  6 variables:
##  $ time     : int  2 2 2 2 4 4 4 4 12 12 ...
##  $ parent   : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte  : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix   : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 1 1 1 1 1 ...
##  $ conc     : num  3.07 3.69 4.7 1.89 7.62 ...
##  $ replicate: int  1 2 3 4 1 2 3 4 1 2 ...

Set time and replicate fields as factors for later statistical inference.

microsome experiment data structure

Check out structure of imported data set for the microsome analysis.

str(microsome)
## 'data.frame':    1123 obs. of  7 variables:
##  $ time     : int  0 0 0 15 15 15 30 30 30 60 ...
##  $ parent   : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte  : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix   : Factor w/ 1 level "microsomes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ conc     : num  1.208 1.596 1.362 0.551 1.347 ...
##  $ replicate: int  1 2 3 1 2 3 1 2 3 1 ...
##  $ microMexp: num  0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 ...

Set time and replicate fields as factors for later statistical inference.

## 'data.frame':    1123 obs. of  7 variables:
##  $ time     : int  0 0 0 15 15 15 30 30 30 60 ...
##  $ parent   : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte  : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix   : Factor w/ 1 level "microsomes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ conc     : num  1.208 1.596 1.362 0.551 1.347 ...
##  $ replicate: Factor w/ 4 levels "1","2","3","4": 1 2 3 1 2 3 1 2 3 1 ...
##  $ microMexp: num  0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 ...

analyze microsomal data

The microsomal experiment has 3-4 replicates for each pesticide. The experiment progressively increases the concentration of the substrate (microMexp) and measures the enzyme velocity. At each substrate concentration the reaction is quenched after a specific period of time (0, 15, 30, 60, 90 mins). This time series data is used to estimate a slope associated with each substrate concentration. Substrate concentration and linear velocity slopes are then fit using Michaelis-Menten kinetics to estimate reaction rates for each pesticide.

atrazine

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  0.712"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.712"       "Concs = 0.712"       "Concs = 0.712"      
##  [4] "Concs = 0.551435364" "Concs = 1.346911275" "Concs = 1.212444791"
##  [7] "Concs = 1.13491833"  "Concs = 1.082466929" "Concs = 1.113889522"
## [10] "Concs = 0.918015161" "Concs = 0.819916078" "Concs = 0.830401682"
## [13] "Concs = 0.60193292"  "Concs = 0.514615471" "Concs = 0.543046503"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.976685    -0.003153  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.37796 -0.22151  0.03239  0.21607  0.41752 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.976685   0.103348   9.450 3.45e-07 ***
## Time[ind]   -0.003153   0.002041  -1.545    0.146    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2554 on 13 degrees of freedom
## Multiple R-squared:  0.1551, Adjusted R-squared:  0.09013 
## F-statistic: 2.387 on 1 and 13 DF,  p-value: 0.1463

##  (Intercept)    Time[ind] 
##  0.976685382 -0.003152627 
##                    2.5 %      97.5 %
## (Intercept)  0.753415733 1.199955031
## Time[ind]   -0.007561078 0.001255824
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
##  [1] "Concs = 10"          "Concs = 10"          "Concs = 10"         
##  [4] "Concs = 8.453642708" "Concs = 7.964608184" "Concs = 7.94451139" 
##  [7] "Concs = 7.680602046" "Concs = 7.527336918" "Concs = 7.478498249"
## [10] "Concs = 5.659397741" "Concs = 6.36413415"  "Concs = 6.660240451"
## [13] "Concs = 6.34249619"  "Concs = 5.477249479" "Concs = 5.670032215"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      9.3056      -0.0475  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.7963 -0.3777 -0.1132  0.5429  0.6944 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  9.305616   0.225240   41.31 3.53e-15 ***
## Time[ind]   -0.047498   0.004733  -10.04 1.73e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5487 on 13 degrees of freedom
## Multiple R-squared:  0.8857, Adjusted R-squared:  0.8769 
## F-statistic: 100.7 on 1 and 13 DF,  p-value: 1.726e-07

## (Intercept)   Time[ind] 
##  9.30561649 -0.04749819 
##                   2.5 %      97.5 %
## (Intercept)  8.81901420  9.79221878
## Time[ind]   -0.05772265 -0.03727374
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  3.1684"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 3.1684"      "Concs = 3.1684"      "Concs = 3.1684"     
##  [4] "Concs = 3.840288882" "Concs = 3.471244145" "Concs = 4.21892194" 
##  [7] "Concs = 3.04149649"  "Concs = 3.107056916" "Concs = 2.539792287"
## [10] "Concs = 2.350740689" "Concs = 2.184285874" "Concs = 1.868856626"
## [13] "Concs = 1.487945081" "Concs = 1.746448606" "Concs = 1.279189407"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     3.60836     -0.02305  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.43996 -0.36681 -0.04111  0.19940  0.95630 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.608360   0.171081  21.091 1.94e-11 ***
## Time[ind]   -0.023049   0.003378  -6.823 1.22e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4227 on 13 degrees of freedom
## Multiple R-squared:  0.7817, Adjusted R-squared:  0.7649 
## F-statistic: 46.56 on 1 and 13 DF,  p-value: 1.218e-05

## (Intercept)   Time[ind] 
##  3.60836007 -0.02304946 
##                   2.5 %      97.5 %
## (Intercept)  3.23876147  3.97795868
## Time[ind]   -0.03034717 -0.01575175
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59" "Indices =  60"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 50"          "Concs = 50"          "Concs = 50"         
##  [4] "Concs = 30.1352595"  "Concs = 28.31360828" "Concs = 26.0438183" 
##  [7] "Concs = 30.34766105" "Concs = 27.74701672" "Concs = 25.6412683" 
## [10] "Concs = 28.51624079" "Concs = 26.35221344" "Concs = 24.78295594"
## [13] "Concs = 26.56519331" "Concs = 24.44743091" "Concs = 24.01565934"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##       39.33        -0.20  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.2839  -5.8864  -0.9746   4.1802  10.6720 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 39.32803    2.97479  13.220 6.49e-09 ***
## Time[ind]   -0.20002    0.05874  -3.405  0.00469 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.35 on 13 degrees of freedom
## Multiple R-squared:  0.4715, Adjusted R-squared:  0.4308 
## F-statistic:  11.6 on 1 and 13 DF,  p-value: 0.004694

## (Intercept)   Time[ind] 
##  39.3280334  -0.2000208 
##                  2.5 %      97.5 %
## (Intercept) 32.9013986 45.75466818
## Time[ind]   -0.3269145 -0.07312715
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  61" "Indices =  62" "Indices =  63" "Indices =  64"
##  [5] "Indices =  65" "Indices =  66" "Indices =  67" "Indices =  68"
##  [9] "Indices =  69" "Indices =  70" "Indices =  71" "Indices =  72"
## [13] "Indices =  73" "Indices =  74" "Indices =  75"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 75"          "Concs = 75"          "Concs = 75"         
##  [4] "Concs = 29.59548976" "Concs = 36.16487256" "Concs = 37.40302159"
##  [7] "Concs = 27.6465584"  "Concs = 28.94210726" "Concs = 34.71955504"
## [10] "Concs = 31.19094038" "Concs = 35.96712185" "Concs = 33.12001232"
## [13] "Concs = 31.51869676" "Concs = 32.99095623" "Concs = 22.85692843"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     54.1995      -0.3519  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -19.325 -12.137   0.036   9.729  20.800 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  54.1995     5.8549   9.257 4.37e-07 ***
## Time[ind]    -0.3519     0.1156  -3.044   0.0094 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14.47 on 13 degrees of freedom
## Multiple R-squared:  0.4162, Adjusted R-squared:  0.3713 
## F-statistic: 9.267 on 1 and 13 DF,  p-value: 0.009404

## (Intercept)   Time[ind] 
##  54.1995284  -0.3519259 
##                 2.5 %     97.5 %
## (Intercept) 41.550828 66.8482288
## Time[ind]   -0.601674 -0.1021778
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  76" "Indices =  77" "Indices =  78" "Indices =  79"
##  [5] "Indices =  80" "Indices =  81" "Indices =  82" "Indices =  83"
##  [9] "Indices =  84" "Indices =  85" "Indices =  86" "Indices =  87"
## [13] "Indices =  88" "Indices =  89" "Indices =  90"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 100"         "Concs = 100"         "Concs = 100"        
##  [4] "Concs = 73.12305661" "Concs = 62.97208244" "Concs = 58.17491784"
##  [7] "Concs = 70.9357471"  "Concs = 60.89975615" "Concs = 54.39425099"
## [10] "Concs = 67.30936536" "Concs = 56.7524779"  "Concs = 50.73568923"
## [13] "Concs = 64.11432499" "Concs = 53.06960934" "Concs = 51.00465026"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     82.6524      -0.3697  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.9313 -10.1962  -0.6243  10.7902  17.3476 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  82.6524     5.3532  15.440 9.66e-10 ***
## Time[ind]    -0.3697     0.1057  -3.498  0.00393 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.23 on 13 degrees of freedom
## Multiple R-squared:  0.4849, Adjusted R-squared:  0.4453 
## F-statistic: 12.24 on 1 and 13 DF,  p-value: 0.003928

## (Intercept)   Time[ind] 
##  82.6523916  -0.3697435 
##                  2.5 %     97.5 %
## (Intercept) 71.0875829 94.2172003
## Time[ind]   -0.5980902 -0.1413968
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  91"  "Indices =  92"  "Indices =  93"  "Indices =  94" 
##  [5] "Indices =  95"  "Indices =  96"  "Indices =  97"  "Indices =  98" 
##  [9] "Indices =  99"  "Indices =  100" "Indices =  101" "Indices =  102"
## [13] "Indices =  103" "Indices =  104"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 15"
##  [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 125"         "Concs = 125"         "Concs = 107.9737675"
##  [4] "Concs = 85.24148342" "Concs = 85.54901737" "Concs = 158.6507932"
##  [7] "Concs = 83.6386001"  "Concs = 83.07467838" "Concs = 170.65218"  
## [10] "Concs = 78.21161933" "Concs = 84.54185693" "Concs = 80.88478508"
## [13] "Concs = 79.00424811" "Concs = 78.20108166"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    114.3266      -0.2991  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -24.599 -20.830  -8.809   7.538  74.269 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 114.3266    13.6528   8.374 2.35e-06 ***
## Time[ind]    -0.2991     0.2604  -1.148    0.273    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 30.85 on 12 degrees of freedom
## Multiple R-squared:  0.099,  Adjusted R-squared:  0.02392 
## F-statistic: 1.319 on 1 and 12 DF,  p-value: 0.2732

## (Intercept)   Time[ind] 
## 114.3266319  -0.2990577 
##                  2.5 %      97.5 %
## (Intercept) 84.5797002 144.0735637
## Time[ind]   -0.8664937   0.2683783
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  105" "Indices =  106" "Indices =  107" "Indices =  108"
##  [5] "Indices =  109" "Indices =  110" "Indices =  111" "Indices =  112"
##  [9] "Indices =  113" "Indices =  114" "Indices =  115" "Indices =  116"
## [13] "Indices =  117" "Indices =  118" "Indices =  119" "Indices =  120"
## [17] "Indices =  121" "Indices =  122" "Indices =  123" "Indices =  124"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15"
##  [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 60" "Times = 90" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 150"         "Concs = 150"         "Concs = 150"        
##  [4] "Concs = 150"         "Concs = 110.8050341" "Concs = 114.7205562"
##  [7] "Concs = 107.1291095" "Concs = 110.2111065" "Concs = 106.4113993"
## [10] "Concs = 109.2588435" "Concs = 108.8110859" "Concs = 98.45121644"
## [13] "Concs = 105.7397626" "Concs = 103.5578664" "Concs = 109.569591" 
## [16] "Concs = 103.2077499" "Concs = 96.26533592" "Concs = 104.9741825"
## [19] "Concs = 105.7942757" "Concs = 95.31462118"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    130.2975      -0.4048  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -19.703 -10.065  -1.362  11.312  19.703 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 130.29755    4.74893  27.437 3.87e-16 ***
## Time[ind]    -0.40478    0.09377  -4.317 0.000415 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.55 on 18 degrees of freedom
## Multiple R-squared:  0.5087, Adjusted R-squared:  0.4814 
## F-statistic: 18.64 on 1 and 18 DF,  p-value: 0.0004153

## (Intercept)   Time[ind] 
## 130.2975485  -0.4047811 
##                   2.5 %      97.5 %
## (Intercept) 120.3204116 140.2746854
## Time[ind]    -0.6017793  -0.2077829
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  125" "Indices =  126" "Indices =  127" "Indices =  128"
##  [5] "Indices =  129" "Indices =  130" "Indices =  131" "Indices =  132"
##  [9] "Indices =  133" "Indices =  134" "Indices =  135" "Indices =  136"
## [13] "Indices =  137" "Indices =  138" "Indices =  139"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 200"         "Concs = 200"         "Concs = 200"        
##  [4] "Concs = 200.8987987" "Concs = 134.815613"  "Concs = 211.5785603"
##  [7] "Concs = 193.1222732" "Concs = 210.4725656" "Concs = 213.5140511"
## [10] "Concs = 197.4425651" "Concs = 146.8087435" "Concs = 201.9011064"
## [13] "Concs = 127.9031459" "Concs = 203.6292232" "Concs = 128.0068329"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    202.5624      -0.4587  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -60.866 -15.397   4.321  22.037  42.350 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 202.5624    11.8464  17.099 2.72e-10 ***
## Time[ind]    -0.4587     0.2339  -1.961   0.0717 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 29.27 on 13 degrees of freedom
## Multiple R-squared:  0.2283, Adjusted R-squared:  0.1689 
## F-statistic: 3.846 on 1 and 13 DF,  p-value: 0.07165

## (Intercept)   Time[ind] 
## 202.5623712  -0.4587044 
##                   2.5 %       97.5 %
## (Intercept) 176.9698580 228.15488441
## Time[ind]    -0.9640276   0.04661879
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  140" "Indices =  141" "Indices =  142" "Indices =  143"
##  [5] "Indices =  144" "Indices =  145" "Indices =  146" "Indices =  147"
##  [9] "Indices =  148" "Indices =  149" "Indices =  150" "Indices =  151"
## [13] "Indices =  152" "Indices =  153" "Indices =  154"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 31" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 250"         "Concs = 250"         "Concs = 250"        
##  [4] "Concs = 111.0650322" "Concs = 110.394181"  "Concs = 107.7699691"
##  [7] "Concs = 110.0390245" "Concs = 133.1636589" "Concs = 106.6453068"
## [10] "Concs = 125.4094086" "Concs = 132.3152295" "Concs = 129.5529012"
## [13] "Concs = 107.9475473" "Concs = 109.2892497" "Concs = 110.9269157"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    181.5297      -0.9871  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -58.954 -43.575   7.248  17.415  68.470 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 181.5297    19.1185   9.495 3.27e-07 ***
## Time[ind]    -0.9871     0.3772  -2.617   0.0213 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 47.18 on 13 degrees of freedom
## Multiple R-squared:  0.345,  Adjusted R-squared:  0.2946 
## F-statistic: 6.848 on 1 and 13 DF,  p-value: 0.02131

## (Intercept)   Time[ind] 
## 181.5296510  -0.9870757 
##                  2.5 %     97.5 %
## (Intercept) 140.226690 222.832612
## Time[ind]    -1.801955  -0.172196
## [1] "##################################################"
## 'data.frame':    10 obs. of  2 variables:
##  $ sub: num  0.712 10 3.168 50 75 ...
##  $ vel: num  15.8 237.5 115.2 1000.1 1759.6 ...
##         sub        vel
## 1    0.7120   15.76313
## 2   10.0000  237.49097
## 3    3.1684  115.24730
## 4   50.0000 1000.10406
## 5   75.0000 1759.62962
## 6  100.0000 1848.71748
## 7  125.0000 1495.28834
## 8  150.0000 2023.90534
## 9  200.0000 2293.52213
## 10 250.0000 4935.37833

We are interested in the reaction rate, v, which is a function of available substrate (pesticide) and the presence of an enzyme. We get Vmax from the asymptote and K = 0.5*Vmax. Biochemical reactions with a single substrate are typically assumed to follow Michaelis-Menten kinetics even if they deviate from the basic model assumptions.

We are fitting the 2-parameter model.

Used to estimate slopes.

dea

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.105334715" "Concs = 0.177716074" "Concs = 0.215668236"
##  [7] "Concs = 0.273065521" "Concs = 0.362248011" "Concs = 0.403265809"
## [10] "Concs = 0.502168642" "Concs = 0.64289193"  "Concs = 0.720570734"
## [13] "Concs = 0.725802164" "Concs = 0.865500124" "Concs = 0.956691847"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.028620     0.009439  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.15230 -0.03367 -0.01260  0.04921  0.12563 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0286203  0.0312329   0.916    0.376    
## Time[ind]   0.0094387  0.0006167  15.305 1.08e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07717 on 13 degrees of freedom
## Multiple R-squared:  0.9474, Adjusted R-squared:  0.9434 
## F-statistic: 234.3 on 1 and 13 DF,  p-value: 1.076e-09

## (Intercept)   Time[ind] 
## 0.028620334 0.009438665 
##                    2.5 %     97.5 %
## (Intercept) -0.038854153 0.09609482
## Time[ind]    0.008106383 0.01077095
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.062527948" "Concs = 0.066722432" "Concs = 0.073739184"
##  [7] "Concs = 0.13417786"  "Concs = 0.142144514" "Concs = 0.153899766"
## [10] "Concs = 0.359398841" "Concs = 0.284549411" "Concs = 0.293488967"
## [13] "Concs = 0.291970799" "Concs = 0.378114427" "Concs = 0.405964967"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.004784     0.004640  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.044227 -0.008723 -0.004784  0.005104  0.076243 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.004784   0.010614   0.451     0.66    
## Time[ind]   0.004640   0.000223  20.804 2.31e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02585 on 13 degrees of freedom
## Multiple R-squared:  0.9708, Adjusted R-squared:  0.9686 
## F-statistic: 432.8 on 1 and 13 DF,  p-value: 2.309e-11

## (Intercept)   Time[ind] 
## 0.004784043 0.004639529 
##                    2.5 %      97.5 %
## (Intercept) -0.018145174 0.027713259
## Time[ind]    0.004157742 0.005121316
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.692469949" "Concs = 0.598237597" "Concs = 0.603481745"
##  [7] "Concs = 1.23886552"  "Concs = 1.156190328" "Concs = 1.011651128"
## [10] "Concs = 2.056702931" "Concs = 1.850305243" "Concs = 1.516060546"
## [13] "Concs = 2.637550555" "Concs = 2.271829323" "Concs = 2.15464298" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.19461      0.02542  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.32748 -0.19461  0.02762  0.14305  0.33708 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.194607   0.086818   2.242   0.0431 *  
## Time[ind]   0.025417   0.001714  14.827 1.59e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2145 on 13 degrees of freedom
## Multiple R-squared:  0.9442, Adjusted R-squared:  0.9399 
## F-statistic: 219.8 on 1 and 13 DF,  p-value: 1.593e-09

## (Intercept)   Time[ind] 
##   0.1946066   0.0254169 
##                   2.5 %     97.5 %
## (Intercept) 0.007046883 0.38216639
## Time[ind]   0.021713543 0.02912026
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59" "Indices =  60"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.126910879" "Concs = 0.194298986" "Concs = 0.205689666"
##  [7] "Concs = 0.343048244" "Concs = 0.344665429" "Concs = 0.433300567"
## [10] "Concs = 0.79823473"  "Concs = 0.910129645" "Concs = 0.789753599"
## [13] "Concs = 1.097803094" "Concs = 1.250836941" "Concs = 0.891346428"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.006856     0.012450  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.235999 -0.032614 -0.006856  0.040146  0.156281 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0068560  0.0371784   0.184    0.857    
## Time[ind]   0.0124499  0.0007341  16.960 3.01e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09186 on 13 degrees of freedom
## Multiple R-squared:  0.9568, Adjusted R-squared:  0.9534 
## F-statistic: 287.6 on 1 and 13 DF,  p-value: 3.008e-10

## (Intercept)   Time[ind] 
##  0.00685602  0.01244988 
##                   2.5 %     97.5 %
## (Intercept) -0.07346298 0.08717502
## Time[ind]    0.01086398 0.01403577
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  61" "Indices =  62" "Indices =  63" "Indices =  64"
##  [5] "Indices =  65" "Indices =  66" "Indices =  67" "Indices =  68"
##  [9] "Indices =  69" "Indices =  70" "Indices =  71" "Indices =  72"
## [13] "Indices =  73"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.660583406" "Concs = 0.521827731" "Concs = 0.519014334"
##  [7] "Concs = 0.937060708" "Concs = 0.947234926" "Concs = 1.586433592"
## [10] "Concs = 1.701961252" "Concs = 2.098184546" "Concs = 2.114078113"
## [13] "Concs = 1.9947066"  
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.15067      0.02247  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.1782 -0.1507  0.0313  0.1123  0.2031 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.150670   0.058446   2.578   0.0257 *  
## Time[ind]   0.022469   0.001143  19.654 6.44e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1406 on 11 degrees of freedom
## Multiple R-squared:  0.9723, Adjusted R-squared:  0.9698 
## F-statistic: 386.3 on 1 and 11 DF,  p-value: 6.445e-10

## (Intercept)   Time[ind] 
##  0.15066966  0.02246945 
##                  2.5 %     97.5 %
## (Intercept) 0.02203109 0.27930823
## Time[ind]   0.01995315 0.02498576
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  0.712"
##  [1] "Indices =  74" "Indices =  75" "Indices =  76" "Indices =  77"
##  [5] "Indices =  78" "Indices =  79" "Indices =  80" "Indices =  81"
##  [9] "Indices =  82" "Indices =  83" "Indices =  84" "Indices =  85"
## [13] "Indices =  86" "Indices =  87"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
##  [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##           0            0  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##      0      0      0      0      0 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)        0          0      NA       NA
## Time[ind]          0          0      NA       NA
## 
## Residual standard error: 0 on 12 degrees of freedom
## Multiple R-squared:    NaN,  Adjusted R-squared:    NaN 
## F-statistic:   NaN on 1 and 12 DF,  p-value: NA

## (Intercept)   Time[ind] 
##           0           0 
##             2.5 % 97.5 %
## (Intercept)     0      0
## Time[ind]       0      0
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  3.1684"
##  [1] "Indices =  88"  "Indices =  89"  "Indices =  90"  "Indices =  91" 
##  [5] "Indices =  92"  "Indices =  93"  "Indices =  94"  "Indices =  95" 
##  [9] "Indices =  96"  "Indices =  97"  "Indices =  98"  "Indices =  99" 
## [13] "Indices =  100" "Indices =  101" "Indices =  102"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [7] "Concs = 0"           "Concs = 0"           "Concs = 0"          
## [10] "Concs = 0.004276181" "Concs = 0"           "Concs = 0"          
## [13] "Concs = 0.068958259" "Concs = 0.095246481" "Concs = 0.042564751"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##  -0.0124160    0.0006791  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.028331 -0.007958  0.002229  0.012416  0.046542 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)   
## (Intercept) -0.0124160  0.0082982  -1.496  0.15847   
## Time[ind]    0.0006791  0.0001638   4.145  0.00115 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0205 on 13 degrees of freedom
## Multiple R-squared:  0.5692, Adjusted R-squared:  0.5361 
## F-statistic: 17.18 on 1 and 13 DF,  p-value: 0.001152

##   (Intercept)     Time[ind] 
## -0.0124160299  0.0006791216 
##                     2.5 %      97.5 %
## (Intercept) -0.0303432318 0.005511172
## Time[ind]    0.0003251496 0.001033094
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  103" "Indices =  104" "Indices =  105" "Indices =  106"
##  [5] "Indices =  107" "Indices =  108" "Indices =  109" "Indices =  110"
##  [9] "Indices =  111" "Indices =  112" "Indices =  113" "Indices =  114"
## [13] "Indices =  115" "Indices =  116" "Indices =  117"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [7] "Concs = 0"           "Concs = 0"           "Concs = 0"          
## [10] "Concs = 0"           "Concs = 0.08814803"  "Concs = 0"          
## [13] "Concs = 0.636612173" "Concs = 0.308057976" "Concs = 0.343301822"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##   -0.076456     0.004313  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.18231 -0.05293  0.01176  0.05403  0.32492 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.076456   0.051227  -1.492 0.159438    
## Time[ind]    0.004313   0.001011   4.264 0.000923 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1266 on 13 degrees of freedom
## Multiple R-squared:  0.5831, Adjusted R-squared:  0.551 
## F-statistic: 18.18 on 1 and 13 DF,  p-value: 0.0009232

##  (Intercept)    Time[ind] 
## -0.076455952  0.004312751 
##                    2.5 %      97.5 %
## (Intercept) -0.187125601 0.034213697
## Time[ind]    0.002127583 0.006497919
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  118" "Indices =  119" "Indices =  120" "Indices =  121"
##  [5] "Indices =  122" "Indices =  123" "Indices =  124" "Indices =  125"
##  [9] "Indices =  126" "Indices =  127" "Indices =  128" "Indices =  129"
## [13] "Indices =  130"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.303186347" "Concs = 0.314346484" "Concs = 0.32890249" 
##  [7] "Concs = 0.470955087" "Concs = 0.418661875" "Concs = 0.69686814" 
## [10] "Concs = 0.65732937"  "Concs = 1.058297138" "Concs = 1.054151944"
## [13] "Concs = 0.826804017"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.08568      0.01013  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.17082 -0.08568  0.02900  0.06552  0.09123 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0856770  0.0366138    2.34   0.0392 *  
## Time[ind]   0.0101327  0.0007162   14.15 2.11e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.08809 on 11 degrees of freedom
## Multiple R-squared:  0.9479, Adjusted R-squared:  0.9432 
## F-statistic: 200.2 on 1 and 11 DF,  p-value: 2.106e-08

## (Intercept)   Time[ind] 
##  0.08567696  0.01013273 
##                   2.5 %     97.5 %
## (Intercept) 0.005090447 0.16626348
## Time[ind]   0.008556376 0.01170909
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  131" "Indices =  132" "Indices =  133" "Indices =  134"
##  [5] "Indices =  135" "Indices =  136" "Indices =  137" "Indices =  138"
##  [9] "Indices =  139" "Indices =  140" "Indices =  141" "Indices =  142"
## [13] "Indices =  143" "Indices =  144" "Indices =  145" "Indices =  146"
## [17] "Indices =  147" "Indices =  148"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15"
##  [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0.651134538" "Concs = 0.410418033"
##  [7] "Concs = 0.72633168"  "Concs = 0.655344167" "Concs = 1.213331632"
## [10] "Concs = 0.938854783" "Concs = 1.336588359" "Concs = 1.220393789"
## [13] "Concs = 2.258618197" "Concs = 2.185187246" "Concs = 2.037689206"
## [16] "Concs = 2.794152863" "Concs = 2.97663412"  "Concs = 2.702787847"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.12001      0.03166  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.26683 -0.12001  0.01248  0.14043  0.26671 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.120012   0.058315   2.058   0.0563 .  
## Time[ind]   0.031662   0.001243  25.467 2.24e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1647 on 16 degrees of freedom
## Multiple R-squared:  0.9759, Adjusted R-squared:  0.9744 
## F-statistic: 648.6 on 1 and 16 DF,  p-value: 2.241e-14

## (Intercept)   Time[ind] 
##  0.12001167  0.03166231 
##                    2.5 %     97.5 %
## (Intercept) -0.003610993 0.24363433
## Time[ind]    0.029026668 0.03429796
## [1] "##################################################"
## 'data.frame':    10 obs. of  2 variables:
##  $ sub: num  50 10 100 75 125 ...
##  $ vel: num  47.2 23.2 127.1 62.2 112.3 ...
##         sub        vel
## 1   50.0000  47.193323
## 2   10.0000  23.197644
## 3  100.0000 127.084516
## 4   75.0000  62.249384
## 5  125.0000 112.347269
## 6    0.7120   0.000000
## 7    3.1684   3.395608
## 8  200.0000  21.563755
## 9  250.0000  50.663660
## 10 150.0000 158.311559

We are interested in the reaction rate, v, which is a function of available substrate (pesticide) and the presence of an enzyme. We get Vmax from the asymptote and K = 0.5*Vmax. Biochemical reactions with a single substrate are typically assumed to follow Michaelis-Menten kinetics even if they deviate from the basic model assumptions.

We are fitting the 2-parameter model.

Used to estimate slopes.

dia

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.17588934"  "Concs = 0.162027282" "Concs = 0.163356559"
##  [7] "Concs = 0.343213005" "Concs = 0.307927387" "Concs = 0.309459105"
## [10] "Concs = 0.560097677" "Concs = 0.54821645"  "Concs = 0.533109282"
## [13] "Concs = 0.73827321"  "Concs = 0.728694143" "Concs = 0.726811372"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.040150     0.008025  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.040150 -0.034677  0.002826  0.026782  0.062303 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0401505  0.0141144   2.845   0.0138 *  
## Time[ind]   0.0080253  0.0002787  28.797 3.67e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03488 on 13 degrees of freedom
## Multiple R-squared:  0.9846, Adjusted R-squared:  0.9834 
## F-statistic: 829.3 on 1 and 13 DF,  p-value: 3.671e-13

## (Intercept)   Time[ind] 
## 0.040150483 0.008025329 
##                   2.5 %      97.5 %
## (Intercept) 0.009658192 0.070642775
## Time[ind]   0.007423260 0.008627398
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.037225886" "Concs = 0.038369499" "Concs = 0.046312162"
##  [7] "Concs = 0.08490015"  "Concs = 0.083838648" "Concs = 0.093345378"
## [10] "Concs = 0.209721193" "Concs = 0.168743119" "Concs = 0.161851994"
## [13] "Concs = 0.162150446" "Concs = 0.222852555" "Concs = 0.229604672"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.004532     0.002650  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.020209 -0.005225 -0.001700  0.001442  0.046169 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0045322  0.0062267   0.728     0.48    
## Time[ind]   0.0026503  0.0001308  20.257 3.23e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01517 on 13 degrees of freedom
## Multiple R-squared:  0.9693, Adjusted R-squared:  0.9669 
## F-statistic: 410.3 on 1 and 13 DF,  p-value: 3.233e-11

## (Intercept)   Time[ind] 
## 0.004532231 0.002650328 
##                    2.5 %      97.5 %
## (Intercept) -0.008919788 0.017984250
## Time[ind]    0.002367676 0.002932981
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.519984026" "Concs = 0.456185794" "Concs = 0.465640368"
##  [7] "Concs = 0.969762496" "Concs = 0.925948373" "Concs = 0.828633383"
## [10] "Concs = 1.646101156" "Concs = 1.493978674" "Concs = 1.273473826"
## [13] "Concs = 2.097846916" "Concs = 1.845660879" "Concs = 1.775884862"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.14326      0.02077  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.23664 -0.14326  0.01084  0.09494  0.25667 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.14326    0.06330   2.263   0.0414 *  
## Time[ind]    0.02077    0.00125  16.617 3.88e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1564 on 13 degrees of freedom
## Multiple R-squared:  0.955,  Adjusted R-squared:  0.9516 
## F-statistic: 276.1 on 1 and 13 DF,  p-value: 3.88e-10

## (Intercept)   Time[ind] 
##  0.14326104  0.02076955 
##                   2.5 %     97.5 %
## (Intercept) 0.006505081 0.28001700
## Time[ind]   0.018069306 0.02346979
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59" "Indices =  60"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.105167732" "Concs = 0.164272494" "Concs = 0.177858813"
##  [7] "Concs = 0.289730134" "Concs = 0.302066953" "Concs = 0.387892352"
## [10] "Concs = 0.703975509" "Concs = 0.8027739"   "Concs = 0.718751156"
## [13] "Concs = 0.974859321" "Concs = 1.104369407" "Concs = 0.769135715"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.003918     0.011012  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.225872 -0.026182 -0.003918  0.046471  0.138129 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0039178  0.0349716   0.112    0.913    
## Time[ind]   0.0110121  0.0006905  15.948 6.47e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.08641 on 13 degrees of freedom
## Multiple R-squared:  0.9514, Adjusted R-squared:  0.9476 
## F-statistic: 254.3 on 1 and 13 DF,  p-value: 6.468e-10

## (Intercept)   Time[ind] 
## 0.003917758 0.011012115 
##                    2.5 %     97.5 %
## (Intercept) -0.071633704 0.07946922
## Time[ind]    0.009520354 0.01250388
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  61" "Indices =  62" "Indices =  63" "Indices =  64"
##  [5] "Indices =  65" "Indices =  66" "Indices =  67" "Indices =  68"
##  [9] "Indices =  69" "Indices =  70" "Indices =  71" "Indices =  72"
## [13] "Indices =  73"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.558156141" "Concs = 0.453398653" "Concs = 0.457441572"
##  [7] "Concs = 0.819739976" "Concs = 0.818340148" "Concs = 1.39707951" 
## [10] "Concs = 1.483198815" "Concs = 1.818559552" "Concs = 1.850457042"
## [13] "Concs = 1.741234977"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.12932      0.01963  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.15472 -0.12932  0.02964  0.10015  0.17613 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.1293156  0.0503960   2.566   0.0262 *  
## Time[ind]   0.0196293  0.0009858  19.912  5.6e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1212 on 11 degrees of freedom
## Multiple R-squared:  0.973,  Adjusted R-squared:  0.9706 
## F-statistic: 396.5 on 1 and 11 DF,  p-value: 5.603e-10

## (Intercept)   Time[ind] 
##   0.1293156   0.0196293 
##                  2.5 %     97.5 %
## (Intercept) 0.01839473 0.24023649
## Time[ind]   0.01745957 0.02179903
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  0.712"
##  [1] "Indices =  74" "Indices =  75" "Indices =  76" "Indices =  77"
##  [5] "Indices =  78" "Indices =  79" "Indices =  80" "Indices =  81"
##  [9] "Indices =  82" "Indices =  83" "Indices =  84" "Indices =  85"
## [13] "Indices =  86" "Indices =  87" "Indices =  88"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
##  [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##           0            0  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##      0      0      0      0      0 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)        0          0      NA       NA
## Time[ind]          0          0      NA       NA
## 
## Residual standard error: 0 on 13 degrees of freedom
## Multiple R-squared:    NaN,  Adjusted R-squared:    NaN 
## F-statistic:   NaN on 1 and 13 DF,  p-value: NA

## (Intercept)   Time[ind] 
##           0           0 
##             2.5 % 97.5 %
## (Intercept)     0      0
## Time[ind]       0      0
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  3.1684"
##  [1] "Indices =  89"  "Indices =  90"  "Indices =  91"  "Indices =  92" 
##  [5] "Indices =  93"  "Indices =  94"  "Indices =  95"  "Indices =  96" 
##  [9] "Indices =  97"  "Indices =  98"  "Indices =  99"  "Indices =  100"
## [13] "Indices =  101" "Indices =  102" "Indices =  103"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
##  [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##           0            0  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##      0      0      0      0      0 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)        0          0      NA       NA
## Time[ind]          0          0      NA       NA
## 
## Residual standard error: 0 on 13 degrees of freedom
## Multiple R-squared:    NaN,  Adjusted R-squared:    NaN 
## F-statistic:   NaN on 1 and 13 DF,  p-value: NA

## (Intercept)   Time[ind] 
##           0           0 
##             2.5 % 97.5 %
## (Intercept)     0      0
## Time[ind]       0      0
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  104" "Indices =  105" "Indices =  106" "Indices =  107"
##  [5] "Indices =  108" "Indices =  109" "Indices =  110" "Indices =  111"
##  [9] "Indices =  112" "Indices =  113" "Indices =  114" "Indices =  115"
## [13] "Indices =  116"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.488073154" "Concs = 0.494203709" "Concs = 0.58569046" 
##  [7] "Concs = 0.731173258" "Concs = 0.714667917" "Concs = 1.145221545"
## [10] "Concs = 1.154181588" "Concs = 1.638731263" "Concs = 1.563749853"
## [13] "Concs = 1.475092589"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.15075      0.01622  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.15075 -0.13584  0.02780  0.09369  0.19157 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.1507544  0.0503259   2.996   0.0122 *  
## Time[ind]   0.0162242  0.0009844  16.481 4.21e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1211 on 11 degrees of freedom
## Multiple R-squared:  0.9611, Adjusted R-squared:  0.9575 
## F-statistic: 271.6 on 1 and 11 DF,  p-value: 4.214e-09

## (Intercept)   Time[ind] 
##   0.1507544   0.0162242 
##                  2.5 %     97.5 %
## (Intercept) 0.03998791 0.26152088
## Time[ind]   0.01405749 0.01839091
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  117" "Indices =  118" "Indices =  119" "Indices =  120"
##  [5] "Indices =  121" "Indices =  122" "Indices =  123" "Indices =  124"
##  [9] "Indices =  125" "Indices =  126" "Indices =  127" "Indices =  128"
## [13] "Indices =  129" "Indices =  130" "Indices =  131" "Indices =  132"
## [17] "Indices =  133" "Indices =  134"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15"
##  [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0.462309631" "Concs = 0.255700106"
##  [7] "Concs = 0.526463046" "Concs = 0.47230486"  "Concs = 0.931548447"
## [10] "Concs = 0.722337549" "Concs = 1.066740758" "Concs = 0.948249061"
## [13] "Concs = 1.827879364" "Concs = 1.789768545" "Concs = 1.614786398"
## [16] "Concs = 2.243971727" "Concs = 2.385364241" "Concs = 2.16439478" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.06633      0.02574  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.21878 -0.06632  0.00304  0.08820  0.22813 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.066325   0.048063    1.38    0.187    
## Time[ind]   0.025743   0.001025   25.12 2.77e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1357 on 16 degrees of freedom
## Multiple R-squared:  0.9753, Adjusted R-squared:  0.9737 
## F-statistic: 631.1 on 1 and 16 DF,  p-value: 2.773e-14

## (Intercept)   Time[ind] 
##   0.0663253   0.0257428 
##                   2.5 %     97.5 %
## (Intercept) -0.03556328 0.16821388
## Time[ind]    0.02357053 0.02791507
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  135" "Indices =  136" "Indices =  137" "Indices =  138"
##  [5] "Indices =  139" "Indices =  140" "Indices =  141" "Indices =  142"
##  [9] "Indices =  143" "Indices =  144" "Indices =  145" "Indices =  146"
## [13] "Indices =  147" "Indices =  148" "Indices =  149"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [7] "Concs = 0"           "Concs = 0"           "Concs = 0"          
## [10] "Concs = 0.147179292" "Concs = 0.49374336"  "Concs = 0.185151589"
## [13] "Concs = 0.905020781" "Concs = 0.751527127" "Concs = 0.778803003"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##   -0.135092     0.009039  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.260068 -0.136078 -0.000493  0.117739  0.226604 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.135092   0.061636  -2.192   0.0472 *  
## Time[ind]    0.009039   0.001217   7.427 4.99e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1523 on 13 degrees of freedom
## Multiple R-squared:  0.8093, Adjusted R-squared:  0.7946 
## F-statistic: 55.16 on 1 and 13 DF,  p-value: 4.994e-06

##  (Intercept)    Time[ind] 
## -0.135091948  0.009038982 
##                    2.5 %       97.5 %
## (Intercept) -0.268247657 -0.001936239
## Time[ind]    0.006409827  0.011668136
## [1] "##################################################"
## 'data.frame':    10 obs. of  2 variables:
##  $ sub: num  50 10 100 75 125 ...
##  $ vel: num  40.1 13.3 103.8 55.1 98.1 ...
##         sub       vel
## 1   50.0000  40.12665
## 2   10.0000  13.25164
## 3  100.0000 103.84774
## 4   75.0000  55.06057
## 5  125.0000  98.14650
## 6    0.7120   0.00000
## 7    3.1684   0.00000
## 8  250.0000  81.12099
## 9  150.0000 128.71399
## 10 200.0000  45.19491

triadimefon

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  0.68082"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.68082"     "Concs = 0.68082"     "Concs = 0.68082"    
##  [4] "Concs = 0.399443695" "Concs = 0.42224169"  "Concs = 0.36799564" 
##  [7] "Concs = 0.335043095" "Concs = 0.307545884" "Concs = 0.33049829" 
## [10] "Concs = 0.298781298" "Concs = 0.300851183" "Concs = 0.297372843"
## [13] "Concs = 0.30988245"  "Concs = 0.29724505"  "Concs = 0.293730776"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.530169    -0.003332  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.12265 -0.08795 -0.03145  0.07331  0.15065 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.5301692  0.0423540  12.518 1.26e-08 ***
## Time[ind]   -0.0033324  0.0008363  -3.985  0.00156 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1047 on 13 degrees of freedom
## Multiple R-squared:  0.5498, Adjusted R-squared:  0.5152 
## F-statistic: 15.88 on 1 and 13 DF,  p-value: 0.001556

##  (Intercept)    Time[ind] 
##  0.530169234 -0.003332387 
##                    2.5 %      97.5 %
## (Intercept)  0.438669087  0.62166938
## Time[ind]   -0.005139054 -0.00152572
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 10"          "Concs = 10"          "Concs = 10"         
##  [4] "Concs = 3.796829723" "Concs = 3.995422538" "Concs = 4.084402023"
##  [7] "Concs = 3.689670522" "Concs = 3.770627455" "Concs = 3.708045842"
## [10] "Concs = 2.923805377" "Concs = 2.81999575"  "Concs = 1.627429272"
## [13] "Concs = 1.556106647" "Concs = 1.615639352"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     7.24520     -0.07209  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.36709 -1.38837 -0.04818  0.86696  2.75480 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  7.24520    0.78504   9.229 8.46e-07 ***
## Time[ind]   -0.07209    0.01573  -4.583 0.000629 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.938 on 12 degrees of freedom
## Multiple R-squared:  0.6364, Adjusted R-squared:  0.6061 
## F-statistic:    21 on 1 and 12 DF,  p-value: 0.0006292

## (Intercept)   Time[ind] 
##  7.24519589 -0.07208527 
##                  2.5 %      97.5 %
## (Intercept)  5.5347334  8.95565838
## Time[ind]   -0.1063558 -0.03781477
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  30" "Indices =  31" "Indices =  32" "Indices =  33"
##  [5] "Indices =  34" "Indices =  35" "Indices =  36" "Indices =  37"
##  [9] "Indices =  38" "Indices =  39" "Indices =  40" "Indices =  41"
## [13] "Indices =  42" "Indices =  43" "Indices =  44"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 2.89"        "Concs = 2.89"        "Concs = 2.89"       
##  [4] "Concs = 1.438977536" "Concs = 1.147878572" "Concs = 1.273836719"
##  [7] "Concs = 1.170628317" "Concs = 1.153347335" "Concs = 0.90609785" 
## [10] "Concs = 0.796555881" "Concs = 0.724314066" "Concs = 0.705525399"
## [13] "Concs = 0.684015583" "Concs = 0.645877009" "Concs = 0.633912406"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     2.10944     -0.01998  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.6618 -0.3636 -0.1861  0.3541  0.7806 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.109439   0.217151   9.714 2.52e-07 ***
## Time[ind]   -0.019984   0.004288  -4.661 0.000446 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5366 on 13 degrees of freedom
## Multiple R-squared:  0.6256, Adjusted R-squared:  0.5968 
## F-statistic: 21.72 on 1 and 13 DF,  p-value: 0.0004457

## (Intercept)   Time[ind] 
##  2.10943918 -0.01998397 
##                   2.5 %      97.5 %
## (Intercept)  1.64031311  2.57856525
## Time[ind]   -0.02924684 -0.01072109
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  45" "Indices =  46" "Indices =  47" "Indices =  48"
##  [5] "Indices =  49" "Indices =  50" "Indices =  51" "Indices =  52"
##  [9] "Indices =  53" "Indices =  54" "Indices =  55" "Indices =  56"
## [13] "Indices =  57"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 50"          "Concs = 50"          "Concs = 50"         
##  [4] "Concs = 25.6223204"  "Concs = 24.15898057" "Concs = 24.97516518"
##  [7] "Concs = 26.62994332" "Concs = 26.25228145" "Concs = 25.95782864"
## [10] "Concs = 28.59868326" "Concs = 22.32352998" "Concs = 22.61126729"
## [13] "Concs = 22.93204565"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     38.6877      -0.2078  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -11.411  -6.200   2.341   2.950  11.312 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 38.68774    3.59860  10.751 3.57e-07 ***
## Time[ind]   -0.20784    0.07039  -2.953   0.0131 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.658 on 11 degrees of freedom
## Multiple R-squared:  0.4421, Adjusted R-squared:  0.3914 
## F-statistic: 8.717 on 1 and 11 DF,  p-value: 0.01315

## (Intercept)   Time[ind] 
##  38.6877394  -0.2078355 
##                  2.5 %      97.5 %
## (Intercept) 30.7672635 46.60821530
## Time[ind]   -0.3627682 -0.05290274
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  58" "Indices =  59" "Indices =  60" "Indices =  61"
##  [5] "Indices =  62" "Indices =  63" "Indices =  64" "Indices =  65"
##  [9] "Indices =  66" "Indices =  67" "Indices =  68" "Indices =  69"
## [13] "Indices =  70" "Indices =  71" "Indices =  72"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 75"          "Concs = 75"          "Concs = 75"         
##  [4] "Concs = 39.60290919" "Concs = 36.37647057" "Concs = 38.41537648"
##  [7] "Concs = 41.36228948" "Concs = 39.60347726" "Concs = 37.05197615"
## [10] "Concs = 38.79077057" "Concs = 39.14694989" "Concs = 38.88285882"
## [13] "Concs = 38.84162326" "Concs = 38.38496898" "Concs = 38.08875118"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     56.5500      -0.2713  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -16.104 -10.084  -1.390   6.479  18.450 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 56.55000    5.05169   11.19 4.79e-08 ***
## Time[ind]   -0.27128    0.09975   -2.72   0.0175 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.48 on 13 degrees of freedom
## Multiple R-squared:  0.3627, Adjusted R-squared:  0.3136 
## F-statistic: 7.397 on 1 and 13 DF,  p-value: 0.01752

## (Intercept)   Time[ind] 
##  56.5500000  -0.2712847 
##                  2.5 %      97.5 %
## (Intercept) 45.6364964 67.46350349
## Time[ind]   -0.4867715 -0.05579803
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  73" "Indices =  74" "Indices =  75" "Indices =  76"
##  [5] "Indices =  77" "Indices =  78" "Indices =  79" "Indices =  80"
##  [9] "Indices =  81" "Indices =  82" "Indices =  83" "Indices =  84"
## [13] "Indices =  85" "Indices =  86" "Indices =  87"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 100"         "Concs = 100"         "Concs = 100"        
##  [4] "Concs = 49.24893567" "Concs = 52.23999837" "Concs = 54.94800062"
##  [7] "Concs = 51.63283427" "Concs = 55.62979138" "Concs = 53.25296347"
## [10] "Concs = 57.2285182"  "Concs = 52.25557462" "Concs = 57.56142454"
## [13] "Concs = 55.15134637" "Concs = 52.80788424" "Concs = 54.77096052"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     75.7963      -0.3252  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -21.6700 -13.5987   0.9416   8.4289  24.2037 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  75.7963     6.6510  11.396 3.87e-08 ***
## Time[ind]    -0.3252     0.1313  -2.476   0.0278 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.43 on 13 degrees of freedom
## Multiple R-squared:  0.3205, Adjusted R-squared:  0.2682 
## F-statistic: 6.131 on 1 and 13 DF,  p-value: 0.02782

## (Intercept)   Time[ind] 
##  75.7962700  -0.3251552 
##                 2.5 %      97.5 %
## (Intercept) 61.427706 90.16483448
## Time[ind]   -0.608862 -0.04144848
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  88"  "Indices =  89"  "Indices =  90"  "Indices =  91" 
##  [5] "Indices =  92"  "Indices =  93"  "Indices =  94"  "Indices =  95" 
##  [9] "Indices =  96"  "Indices =  97"  "Indices =  98"  "Indices =  99" 
## [13] "Indices =  100" "Indices =  101"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 125"         "Concs = 125"         "Concs = 125"        
##  [4] "Concs = 54.97761564" "Concs = 64.19295623" "Concs = 61.97688614"
##  [7] "Concs = 68.89112849" "Concs = 56.33566744" "Concs = 71.31751913"
## [10] "Concs = 66.04862513" "Concs = 69.71262134" "Concs = 57.48171016"
## [13] "Concs = 60.79276739" "Concs = 57.42314849"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     94.1185      -0.4829  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -31.898 -19.697   2.735   9.305  30.881 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  94.1185     9.0233  10.431 2.27e-07 ***
## Time[ind]    -0.4829     0.1808  -2.671   0.0204 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 22.28 on 12 degrees of freedom
## Multiple R-squared:  0.3728, Adjusted R-squared:  0.3206 
## F-statistic: 7.134 on 1 and 12 DF,  p-value: 0.02038

## (Intercept)   Time[ind] 
##  94.1185302  -0.4828739 
##                  2.5 %       97.5 %
## (Intercept) 74.4584918 113.77856852
## Time[ind]   -0.8767787  -0.08896906
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  102" "Indices =  103" "Indices =  104" "Indices =  105"
##  [5] "Indices =  106" "Indices =  107" "Indices =  108" "Indices =  109"
##  [9] "Indices =  110" "Indices =  111" "Indices =  112" "Indices =  113"
## [13] "Indices =  114" "Indices =  115"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 15"
##  [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 150"         "Concs = 150"         "Concs = 78.63355587"
##  [4] "Concs = 62.93987056" "Concs = 106.7018113" "Concs = 73.37624336"
##  [7] "Concs = 66.9635187"  "Concs = 95.5133834"  "Concs = 69.7678651" 
## [10] "Concs = 58.53815945" "Concs = 61.06336245" "Concs = 82.43537943"
## [13] "Concs = 75.76324133" "Concs = 73.77914496"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    107.9411      -0.5226  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -37.163 -18.678  -1.785  14.357  42.059 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 107.9411    11.3512   9.509 6.15e-07 ***
## Time[ind]    -0.5226     0.2165  -2.413   0.0327 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 25.65 on 12 degrees of freedom
## Multiple R-squared:  0.3268, Adjusted R-squared:  0.2707 
## F-statistic: 5.824 on 1 and 12 DF,  p-value: 0.03271

## (Intercept)   Time[ind] 
## 107.9411403  -0.5225648 
##                  2.5 %       97.5 %
## (Intercept) 83.2090866 132.67319401
## Time[ind]   -0.9943398  -0.05078988
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  116" "Indices =  117" "Indices =  118" "Indices =  119"
##  [5] "Indices =  120" "Indices =  121" "Indices =  122" "Indices =  123"
##  [9] "Indices =  124" "Indices =  125" "Indices =  126" "Indices =  127"
## [13] "Indices =  128" "Indices =  129" "Indices =  130"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 200"         "Concs = 200"         "Concs = 200"        
##  [4] "Concs = 338.7826757" "Concs = 357.9520843" "Concs = 202.0964578"
##  [7] "Concs = 422.3552358" "Concs = 340.5253492" "Concs = 345.8291382"
## [10] "Concs = 359.4674526" "Concs = 377.2730298" "Concs = 186.1093226"
## [13] "Concs = 471.6047045" "Concs = 376.1365036" "Concs = 190.6933116"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      261.28         1.11  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -170.53  -61.28   31.56   56.04  127.76 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 261.2807    37.7669   6.918 1.06e-05 ***
## Time[ind]     1.1105     0.7457   1.489     0.16    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 93.32 on 13 degrees of freedom
## Multiple R-squared:  0.1457, Adjusted R-squared:  0.08001 
## F-statistic: 2.217 on 1 and 13 DF,  p-value: 0.1603

## (Intercept)   Time[ind] 
##  261.280745    1.110451 
##                   2.5 %     97.5 %
## (Intercept) 179.6902783 342.871211
## Time[ind]    -0.5005493   2.721452
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  131" "Indices =  132" "Indices =  133" "Indices =  134"
##  [5] "Indices =  135" "Indices =  136" "Indices =  137" "Indices =  138"
##  [9] "Indices =  139" "Indices =  140" "Indices =  141" "Indices =  142"
## [13] "Indices =  143" "Indices =  144"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 15"
##  [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 250"         "Concs = 250"         "Concs = 186.8824662"
##  [4] "Concs = 208.9457498" "Concs = 167.0779465" "Concs = 229.5166359"
##  [7] "Concs = 99.11335239" "Concs = 263.0350796" "Concs = 59.52448054"
## [10] "Concs = 46.29054385" "Concs = 51.98182232" "Concs = 162.0360626"
## [13] "Concs = 200.5560551" "Concs = 187.8908429"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    209.0664      -0.9642  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -104.92  -67.65   27.05   47.27   82.90 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 209.0664    31.6894   6.597 2.55e-05 ***
## Time[ind]    -0.9642     0.6045  -1.595    0.137    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 71.6 on 12 degrees of freedom
## Multiple R-squared:  0.1749, Adjusted R-squared:  0.1062 
## F-statistic: 2.544 on 1 and 12 DF,  p-value: 0.1367

## (Intercept)   Time[ind] 
## 209.0664272  -0.9642375 
##                  2.5 %      97.5 %
## (Intercept) 140.021166 278.1116888
## Time[ind]    -2.281307   0.3528317
## [1] "##################################################"
## 'data.frame':    10 obs. of  2 variables:
##  $ sub: num  0.681 10 2.89 50 75 ...
##  $ vel: num  16.7 360.4 99.9 1039.2 1356.4 ...
##          sub         vel
## 1    0.68082    16.66194
## 2   10.00000   360.42636
## 3    2.89000    99.91984
## 4   50.00000  1039.17744
## 5   75.00000  1356.42374
## 6  100.00000  1625.77622
## 7  125.00000  2414.36930
## 8  150.00000  2612.82417
## 9  200.00000 -5552.25724
## 10 250.00000  4821.18755

tdla

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  0.68"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.124349504" "Concs = 0.14627783"  "Concs = 0.089752887"
##  [7] "Concs = 0.107638677" "Concs = 0.159434476" "Concs = 0.159787554"
## [10] "Concs = 0.099828091" "Concs = 0.225228369" "Concs = 0.139329405"
## [13] "Concs = 0.072482112" "Concs = 0.09994686"  "Concs = 0.061506341"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.076146     0.000587  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.076146 -0.061979  0.004803  0.050363  0.113865 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 0.0761457  0.0260993   2.918    0.012 *
## Time[ind]   0.0005870  0.0005153   1.139    0.275  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.06449 on 13 degrees of freedom
## Multiple R-squared:  0.09074,    Adjusted R-squared:  0.0208 
## F-statistic: 1.297 on 1 and 13 DF,  p-value: 0.2753

##  (Intercept)    Time[ind] 
## 0.0761456879 0.0005869689 
##                     2.5 %     97.5 %
## (Intercept)  0.0197616122 0.13252976
## Time[ind]   -0.0005263326 0.00170027
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.562008549" "Concs = 0.514503123" "Concs = 0.553400833"
##  [7] "Concs = 0.914781067" "Concs = 0.896944628" "Concs = 0.854682343"
## [10] "Concs = 0.640465968" "Concs = 1.46510307"  "Concs = 1.529173181"
## [13] "Concs = 1.670981262" "Concs = 1.594325825" "Concs = 1.598291535"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.20234      0.01668  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.56286 -0.15591  0.06192  0.17298  0.32585 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.202336   0.098508   2.054   0.0607 .  
## Time[ind]   0.016683   0.001945   8.577 1.03e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2434 on 13 degrees of freedom
## Multiple R-squared:  0.8498, Adjusted R-squared:  0.8383 
## F-statistic: 73.57 on 1 and 13 DF,  p-value: 1.034e-06

## (Intercept)   Time[ind] 
##  0.20233603  0.01668311 
##                   2.5 %    97.5 %
## (Intercept) -0.01047689 0.4151490
## Time[ind]    0.01248113 0.0208851
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.587769932" "Concs = 0.500911907" "Concs = 2.390614252"
##  [7] "Concs = 0.732569141" "Concs = 0.819349521" "Concs = 0.882196657"
## [10] "Concs = 1.272480799" "Concs = 1.332879865" "Concs = 1.171215513"
## [13] "Concs = 1.284978616" "Concs = 1.466507839"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.45047      0.01239  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.45047 -0.24456 -0.06916  0.04420  1.75424 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 0.450472   0.232029   1.941   0.0761 .
## Time[ind]   0.012394   0.004981   2.488   0.0285 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5652 on 12 degrees of freedom
## Multiple R-squared:  0.3403, Adjusted R-squared:  0.2853 
## F-statistic:  6.19 on 1 and 12 DF,  p-value: 0.02854

## (Intercept)   Time[ind] 
##  0.45047221  0.01239366 
##                    2.5 %    97.5 %
## (Intercept) -0.055074499 0.9560189
## Time[ind]    0.001540229 0.0232471
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  45" "Indices =  46" "Indices =  47" "Indices =  48"
##  [5] "Indices =  49" "Indices =  50" "Indices =  51" "Indices =  52"
##  [9] "Indices =  53" "Indices =  54" "Indices =  55" "Indices =  56"
## [13] "Indices =  57" "Indices =  58" "Indices =  59"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.366202494" "Concs = 2.316676352" "Concs = 2.98040696" 
##  [7] "Concs = 2.746818134" "Concs = 3.431666105" "Concs = 3.294563534"
## [10] "Concs = 3.820882667" "Concs = 4.627112685" "Concs = 4.219456142"
## [13] "Concs = 4.7035697"   "Concs = 4.419483485" "Concs = 4.677842802"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     1.16198      0.04474  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1620 -0.6402  0.2425  0.6568  1.1473 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.161976   0.341679   3.401  0.00474 ** 
## Time[ind]   0.044744   0.006746   6.632 1.63e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8442 on 13 degrees of freedom
## Multiple R-squared:  0.7719, Adjusted R-squared:  0.7543 
## F-statistic: 43.99 on 1 and 13 DF,  p-value: 1.632e-05

## (Intercept)   Time[ind] 
##  1.16197557  0.04474367 
##                  2.5 %     97.5 %
## (Intercept) 0.42382326 1.90012788
## Time[ind]   0.03016888 0.05931846
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  60" "Indices =  61" "Indices =  62" "Indices =  63"
##  [5] "Indices =  64" "Indices =  65" "Indices =  66" "Indices =  67"
##  [9] "Indices =  68" "Indices =  69" "Indices =  70" "Indices =  71"
## [13] "Indices =  72" "Indices =  73" "Indices =  74"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.219185884" "Concs = 2.155328801" "Concs = 2.202708256"
##  [7] "Concs = 2.811019032" "Concs = 2.229132105" "Concs = 2.319209877"
## [10] "Concs = 3.438186485" "Concs = 3.239731804" "Concs = 3.112249253"
## [13] "Concs = 3.973569475" "Concs = 3.922150065" "Concs = 3.990347195"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.91058      0.03753  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.91058 -0.34028  0.07745  0.48230  0.77459 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.910579   0.255061   3.570  0.00342 ** 
## Time[ind]   0.037528   0.005036   7.452 4.82e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6302 on 13 degrees of freedom
## Multiple R-squared:  0.8103, Adjusted R-squared:  0.7957 
## F-statistic: 55.53 on 1 and 13 DF,  p-value: 4.822e-06

## (Intercept)   Time[ind] 
##  0.91057884  0.03752844 
##                  2.5 %     97.5 %
## (Intercept) 0.35955278 1.46160490
## Time[ind]   0.02664845 0.04840843
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  75" "Indices =  76" "Indices =  77" "Indices =  78"
##  [5] "Indices =  79" "Indices =  80" "Indices =  81" "Indices =  82"
##  [9] "Indices =  83" "Indices =  84" "Indices =  85" "Indices =  86"
## [13] "Indices =  87" "Indices =  88" "Indices =  89"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.973173898" "Concs = 4.278761105" "Concs = 5.203600328"
##  [7] "Concs = 3.752087918" "Concs = 4.489689601" "Concs = 4.3820044"  
## [10] "Concs = 4.18858056"  "Concs = 4.787062374" "Concs = 4.819935077"
## [13] "Concs = 5.229225315" "Concs = 5.541134166" "Concs = 5.363637277"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      1.9240       0.0447  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9240 -0.6505  0.1811  0.8021  2.6091 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  1.92398    0.56293   3.418  0.00458 **
## Time[ind]    0.04470    0.01111   4.022  0.00145 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.391 on 13 degrees of freedom
## Multiple R-squared:  0.5544, Adjusted R-squared:  0.5201 
## F-statistic: 16.17 on 1 and 13 DF,  p-value: 0.001452

## (Intercept)   Time[ind] 
##  1.92397917  0.04469949 
##                 2.5 %     97.5 %
## (Intercept) 0.7078516 3.14010672
## Time[ind]   0.0206871 0.06871189
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  90"  "Indices =  91"  "Indices =  92"  "Indices =  93" 
##  [5] "Indices =  94"  "Indices =  95"  "Indices =  96"  "Indices =  97" 
##  [9] "Indices =  98"  "Indices =  99"  "Indices =  100" "Indices =  101"
## [13] "Indices =  102" "Indices =  103" "Indices =  104"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 3.664975002" "Concs = 5.128116042" "Concs = 3.342678541"
##  [7] "Concs = 3.909877303" "Concs = 3.131834777" "Concs = 6.184369077"
## [10] "Concs = 5.034115174" "Concs = 6.997125798" "Concs = 5.513028895"
## [13] "Concs = 5.609126979" "Concs = 6.565737598" "Concs = 6.051117386"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     1.86482      0.05668  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8648 -1.1362 -0.2317  0.7887  2.6191 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.86482    0.62163   3.000 0.010241 *  
## Time[ind]    0.05668    0.01227   4.618 0.000482 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.536 on 13 degrees of freedom
## Multiple R-squared:  0.6213, Adjusted R-squared:  0.5922 
## F-statistic: 21.33 on 1 and 13 DF,  p-value: 0.0004816

## (Intercept)   Time[ind] 
##  1.86482214  0.05668337 
##                  2.5 %     97.5 %
## (Intercept) 0.52186968 3.20777461
## Time[ind]   0.03016682 0.08319991
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  105" "Indices =  106" "Indices =  107" "Indices =  108"
##  [5] "Indices =  109" "Indices =  110" "Indices =  111" "Indices =  112"
##  [9] "Indices =  113" "Indices =  114" "Indices =  115" "Indices =  116"
## [13] "Indices =  117" "Indices =  118" "Indices =  119"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 4.690841414" "Concs = 4.417155339" "Concs = 6.21277087" 
##  [7] "Concs = 3.839544319" "Concs = 4.519625245" "Concs = 6.760429619"
## [10] "Concs = 7.2240805"   "Concs = 3.468203577" "Concs = 4.462789205"
## [13] "Concs = 8.035064896" "Concs = 8.748204845" "Concs = 7.504701282"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     2.03606      0.06725  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.6030 -1.8222 -0.0537  1.2626  3.1679 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.03606    0.76233   2.671 0.019234 *  
## Time[ind]    0.06725    0.01505   4.468 0.000633 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.884 on 13 degrees of freedom
## Multiple R-squared:  0.6056, Adjusted R-squared:  0.5753 
## F-statistic: 19.96 on 1 and 13 DF,  p-value: 0.0006335

## (Intercept)   Time[ind] 
##  2.03606128  0.06725212 
##                  2.5 %     97.5 %
## (Intercept) 0.38913806 3.68298450
## Time[ind]   0.03473369 0.09977056
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  120" "Indices =  121" "Indices =  122" "Indices =  123"
##  [5] "Indices =  124" "Indices =  125" "Indices =  126" "Indices =  127"
##  [9] "Indices =  128" "Indices =  129" "Indices =  130"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 30"
##  [6] "Times = 30" "Times = 60" "Times = 60" "Times = 60" "Times = 90"
## [11] "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 17.81066063"
##  [4] "Concs = 14.08273374" "Concs = 20.76679639" "Concs = 16.9957259" 
##  [7] "Concs = 18.08230553" "Concs = 16.51635254" "Concs = 17.9065353" 
## [10] "Concs = 19.61630031" "Concs = 17.39520371"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      8.5041       0.1458  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.5041 -3.1238  0.6521  3.7537  7.8875 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  8.50414    2.90485   2.928   0.0168 *
## Time[ind]    0.14584    0.05633   2.589   0.0293 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.865 on 9 degrees of freedom
## Multiple R-squared:  0.4268, Adjusted R-squared:  0.3632 
## F-statistic: 6.702 on 1 and 9 DF,  p-value: 0.02927

## (Intercept)   Time[ind] 
##    8.504137    0.145838 
##                  2.5 %     97.5 %
## (Intercept) 1.93290585 15.0753686
## Time[ind]   0.01840552  0.2732705
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  0.68 10 2.89 50 75 100 125 150 250
##  $ vel: num  2.93 83.42 61.97 223.72 187.64 ...
##      sub        vel
## 1   0.68   2.934844
## 2  10.00  83.415563
## 3   2.89  61.968314
## 4  50.00 223.718355
## 5  75.00 187.642185
## 6 100.00 223.497474
## 7 125.00 283.416841
## 8 150.00 336.260615
## 9 250.00 729.190051

tdlb

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  0.68"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.159849035" "Concs = 0.171671782" "Concs = 0.137258352"
##  [7] "Concs = 0.135498718" "Concs = 0.166579942" "Concs = 0.160555121"
## [10] "Concs = 0.085155894" "Concs = 0.137641779" "Concs = 0.101223849"
## [13] "Concs = 0.041122976" "Concs = 0.056120989" "Concs = 0.040770384"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##   0.0968096   -0.0001003  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.09681 -0.04683  0.01043  0.05570  0.07637 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  0.0968096  0.0272858   3.548  0.00357 **
## Time[ind]   -0.0001003  0.0005388  -0.186  0.85514   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.06742 on 13 degrees of freedom
## Multiple R-squared:  0.002661,   Adjusted R-squared:  -0.07406 
## F-statistic: 0.03468 on 1 and 13 DF,  p-value: 0.8551

##   (Intercept)     Time[ind] 
##  0.0968095889 -0.0001003334 
##                    2.5 %      97.5 %
## (Intercept)  0.037862112 0.155757066
## Time[ind]   -0.001264249 0.001063582
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.540578005" "Concs = 0.535327972" "Concs = 0.549947891"
##  [7] "Concs = 0.963906807" "Concs = 0.939249694" "Concs = 0.8832653"  
## [10] "Concs = 0.462660817" "Concs = 1.424227752" "Concs = 1.466547242"
## [13] "Concs = 1.470094516" "Concs = 1.424845158" "Concs = 1.471282702"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.23849      0.01462  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.65322 -0.18411  0.07749  0.23407  0.35066 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.238486   0.115619   2.063   0.0597 .  
## Time[ind]   0.014623   0.002283   6.406 2.32e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2857 on 13 degrees of freedom
## Multiple R-squared:  0.7594, Adjusted R-squared:  0.7409 
## F-statistic: 41.03 on 1 and 13 DF,  p-value: 2.323e-05

## (Intercept)   Time[ind] 
##  0.23848608  0.01462332 
##                    2.5 %     97.5 %
## (Intercept) -0.011292644 0.48826480
## Time[ind]    0.009691449 0.01955519
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.502687773" "Concs = 0.443748362" "Concs = 1.739413295"
##  [7] "Concs = 0.631006803" "Concs = 0.676925019" "Concs = 0.712219102"
## [10] "Concs = 0.887492395" "Concs = 0.922424215" "Concs = 0.774293903"
## [13] "Concs = 0.733501521" "Concs = 0.837366651" "Concs = 0.76078022" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.415973     0.005782  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.41597 -0.18918 -0.00001  0.10515  1.23672 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 0.415973   0.166466   2.499   0.0266 *
## Time[ind]   0.005782   0.003287   1.759   0.1021  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4113 on 13 degrees of freedom
## Multiple R-squared:  0.1923, Adjusted R-squared:  0.1301 
## F-statistic: 3.094 on 1 and 13 DF,  p-value: 0.1021

## (Intercept)   Time[ind] 
## 0.415972672 0.005781657 
##                    2.5 %     97.5 %
## (Intercept)  0.056345267 0.77560008
## Time[ind]   -0.001319173 0.01288249
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59" "Indices =  60"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.598887073" "Concs = 2.355603277" "Concs = 3.141649164"
##  [7] "Concs = 3.674320887" "Concs = 4.289723095" "Concs = 4.280136564"
## [10] "Concs = 6.243599629" "Concs = 6.734010485" "Concs = 6.361017452"
## [13] "Concs = 7.195467955" "Concs = 6.834134189" "Concs = 6.9532999"  
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     1.12601      0.07482  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1260 -0.9664  0.3036  0.8195  1.1186 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.126011   0.372593   3.022  0.00981 ** 
## Time[ind]   0.074823   0.007357  10.171 1.48e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9206 on 13 degrees of freedom
## Multiple R-squared:  0.8884, Adjusted R-squared:  0.8798 
## F-statistic: 103.4 on 1 and 13 DF,  p-value: 1.478e-07

## (Intercept)   Time[ind] 
##  1.12601129  0.07482339 
##                  2.5 %     97.5 %
## (Intercept) 0.32107348 1.93094910
## Time[ind]   0.05892992 0.09071685
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  61" "Indices =  62" "Indices =  63" "Indices =  64"
##  [5] "Indices =  65" "Indices =  66" "Indices =  67" "Indices =  68"
##  [9] "Indices =  69" "Indices =  70" "Indices =  71" "Indices =  72"
## [13] "Indices =  73" "Indices =  74" "Indices =  75"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.526757358" "Concs = 2.313637237" "Concs = 2.49086012" 
##  [7] "Concs = 3.789628052" "Concs = 3.174642429" "Concs = 3.191438558"
## [10] "Concs = 5.432233942" "Concs = 4.969157891" "Concs = 5.064503301"
## [13] "Concs = 6.712664257" "Concs = 6.597464296" "Concs = 6.484914"   
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.85930      0.06813  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.8593 -0.4502  0.1172  0.4586  0.8863 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.859298   0.247735   3.469  0.00416 ** 
## Time[ind]   0.068134   0.004892  13.929 3.43e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6121 on 13 degrees of freedom
## Multiple R-squared:  0.9372, Adjusted R-squared:  0.9324 
## F-statistic:   194 on 1 and 13 DF,  p-value: 3.431e-09

## (Intercept)   Time[ind] 
##  0.85929819  0.06813407 
##                  2.5 %     97.5 %
## (Intercept) 0.32409874 1.39449763
## Time[ind]   0.05756657 0.07870156
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  76" "Indices =  77" "Indices =  78" "Indices =  79"
##  [5] "Indices =  80" "Indices =  81" "Indices =  82" "Indices =  83"
##  [9] "Indices =  84" "Indices =  85" "Indices =  86" "Indices =  87"
## [13] "Indices =  88" "Indices =  89" "Indices =  90"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.987986855" "Concs = 4.62322369"  "Concs = 5.738654903"
##  [7] "Concs = 5.010985215" "Concs = 6.920302664" "Concs = 6.308852644"
## [10] "Concs = 8.11715413"  "Concs = 8.804687457" "Concs = 8.950282552"
## [13] "Concs = 10.81651263" "Concs = 11.45788264" "Concs = 11.01782631"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      1.6755       0.1122  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.6755 -0.8540 -0.2888  0.9047  2.3806 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.67547    0.53930   3.107  0.00834 ** 
## Time[ind]    0.11217    0.01065  10.534  9.8e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.333 on 13 degrees of freedom
## Multiple R-squared:  0.8951, Adjusted R-squared:  0.8871 
## F-statistic:   111 on 1 and 13 DF,  p-value: 9.803e-08

## (Intercept)   Time[ind] 
##    1.675467    0.112175 
##                  2.5 %    97.5 %
## (Intercept) 0.51037689 2.8405565
## Time[ind]   0.08917031 0.1351796
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  91"  "Indices =  92"  "Indices =  93"  "Indices =  94" 
##  [5] "Indices =  95"  "Indices =  96"  "Indices =  97"  "Indices =  98" 
##  [9] "Indices =  99"  "Indices =  100" "Indices =  101" "Indices =  102"
## [13] "Indices =  103" "Indices =  104" "Indices =  105"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 4.759629498" "Concs = 6.081131385" "Concs = 4.761075887"
##  [7] "Concs = 6.970865526" "Concs = 5.864292522" "Concs = 8.990170569"
## [10] "Concs = 10.29254833" "Concs = 11.89986315" "Concs = 10.55439287"
## [13] "Concs = 12.66145718" "Concs = 13.84087365" "Concs = 12.77355717"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      2.0173       0.1354  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0173 -1.4830  0.1531  0.8029  2.9118 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.01726    0.65938   3.059  0.00913 ** 
## Time[ind]    0.13537    0.01302  10.397 1.14e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.629 on 13 degrees of freedom
## Multiple R-squared:  0.8927, Adjusted R-squared:  0.8844 
## F-statistic: 108.1 on 1 and 13 DF,  p-value: 1.143e-07

## (Intercept)   Time[ind] 
##   2.0172597   0.1353692 
##                 2.5 %   97.5 %
## (Intercept) 0.5927540 3.441765
## Time[ind]   0.1072424 0.163496
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  106" "Indices =  107" "Indices =  108" "Indices =  109"
##  [5] "Indices =  110" "Indices =  111" "Indices =  112" "Indices =  113"
##  [9] "Indices =  114" "Indices =  115" "Indices =  116" "Indices =  117"
## [13] "Indices =  118" "Indices =  119" "Indices =  120"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 6.090475637" "Concs = 5.80525893"  "Concs = 8.98551562" 
##  [7] "Concs = 6.941039356" "Concs = 7.206821805" "Concs = 10.94796175"
## [10] "Concs = 13.80091931" "Concs = 7.457397291" "Concs = 9.668427529"
## [13] "Concs = 16.81467648" "Concs = 18.96446187" "Concs = 16.539466"  
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      2.1629       0.1654  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.6315 -2.1629 -0.1849  1.5790  4.3411 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.16290    1.03599   2.088   0.0571 .  
## Time[ind]    0.16543    0.02046   8.087 1.98e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.56 on 13 degrees of freedom
## Multiple R-squared:  0.8342, Adjusted R-squared:  0.8214 
## F-statistic: 65.41 on 1 and 13 DF,  p-value: 1.985e-06

## (Intercept)   Time[ind] 
##   2.1628981   0.1654341 
##                   2.5 %    97.5 %
## (Intercept) -0.07522754 4.4010238
## Time[ind]    0.12124239 0.2096258
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  121" "Indices =  122" "Indices =  123" "Indices =  124"
##  [5] "Indices =  125" "Indices =  126" "Indices =  127" "Indices =  128"
##  [9] "Indices =  129" "Indices =  130" "Indices =  131"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 30"
##  [6] "Times = 30" "Times = 60" "Times = 60" "Times = 60" "Times = 90"
## [11] "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 22.19280552"
##  [4] "Concs = 17.62020275" "Concs = 24.15778887" "Concs = 20.49970666"
##  [7] "Concs = 25.33183553" "Concs = 23.63873667" "Concs = 25.85088774"
## [10] "Concs = 28.34728168" "Concs = 25.77673742"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      9.7157       0.2368  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -9.716 -3.962  1.410  4.017  8.926 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  9.71573    3.28235    2.96  0.01596 * 
## Time[ind]    0.23676    0.06365    3.72  0.00477 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.628 on 9 degrees of freedom
## Multiple R-squared:  0.6059, Adjusted R-squared:  0.5621 
## F-statistic: 13.84 on 1 and 9 DF,  p-value: 0.004774

## (Intercept)   Time[ind] 
##    9.715734    0.236762 
##                  2.5 %    97.5 %
## (Intercept) 2.29053916 17.140929
## Time[ind]   0.09276905  0.380755
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  0.68 10 2.89 50 75 100 125 150 250
##  $ vel: num  -0.502 73.117 28.908 374.117 340.67 ...
##      sub          vel
## 1   0.68   -0.5016668
## 2  10.00   73.1166041
## 3   2.89   28.9082836
## 4  50.00  374.1169252
## 5  75.00  340.6703300
## 6 100.00  560.8747995
## 7 125.00  676.8458299
## 8 150.00  827.1705102
## 9 250.00 1183.8100663

fipronil

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 10"          "Concs = 10"          "Concs = 10"         
##  [4] "Concs = 7.601993848" "Concs = 11.87171779" "Concs = 8.347482218"
##  [7] "Concs = 12.54233702" "Concs = 9.213313367" "Concs = 10.38856477"
## [10] "Concs = 12.36949156" "Concs = 8.215365646" "Concs = 11.17931895"
## [13] "Concs = 12.71923746" "Concs = 9.99477721" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     9.71360      0.01483  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3880 -1.0265  0.2087  1.3248  2.3838 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  9.71360    0.69685  13.939 8.96e-09 ***
## Time[ind]    0.01483    0.01333   1.112    0.288    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.635 on 12 degrees of freedom
## Multiple R-squared:  0.09348,    Adjusted R-squared:  0.01794 
## F-statistic: 1.237 on 1 and 12 DF,  p-value: 0.2878

## (Intercept)   Time[ind] 
##   9.7136033   0.0148301 
##                  2.5 %      97.5 %
## (Intercept)  8.1953041 11.23190240
## Time[ind]   -0.0142172  0.04387739
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  15" "Indices =  16" "Indices =  17" "Indices =  18"
##  [5] "Indices =  19" "Indices =  20" "Indices =  21" "Indices =  22"
##  [9] "Indices =  23" "Indices =  24" "Indices =  25" "Indices =  26"
## [13] "Indices =  27" "Indices =  28" "Indices =  29"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 2.89"        "Concs = 2.89"        "Concs = 2.89"       
##  [4] "Concs = 0.961731316" "Concs = 0.608701865" "Concs = 2.021395291"
##  [7] "Concs = 0.34095865"  "Concs = 1.416552854" "Concs = 4.678731136"
## [10] "Concs = 1.597568113" "Concs = 2.059112975" "Concs = 4.336224939"
## [13] "Concs = 0.73593197"  "Concs = 1.01143428"  "Concs = 2.098949857"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    2.330304    -0.007551  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7628 -0.8010 -0.1956  0.5597  2.5749 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.330304   0.537794   4.333 0.000812 ***
## Time[ind]   -0.007551   0.010619  -0.711 0.489590    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.329 on 13 degrees of freedom
## Multiple R-squared:  0.03744,    Adjusted R-squared:  -0.0366 
## F-statistic: 0.5057 on 1 and 13 DF,  p-value: 0.4896

##  (Intercept)    Time[ind] 
##  2.330304214 -0.007550889 
##                   2.5 %     97.5 %
## (Intercept)  1.16847156 3.49213686
## Time[ind]   -0.03049123 0.01538945
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  30" "Indices =  31" "Indices =  32" "Indices =  33"
##  [5] "Indices =  34" "Indices =  35" "Indices =  36" "Indices =  37"
##  [9] "Indices =  38" "Indices =  39" "Indices =  40" "Indices =  41"
## [13] "Indices =  42" "Indices =  43" "Indices =  44"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 50"          "Concs = 50"          "Concs = 50"         
##  [4] "Concs = 223.3849191" "Concs = 19.09530124" "Concs = 61.85004879"
##  [7] "Concs = 76.72890033" "Concs = 65.4447593"  "Concs = 59.88633813"
## [10] "Concs = 74.09066447" "Concs = 65.54242812" "Concs = 39.55208359"
## [13] "Concs = 66.15498564" "Concs = 23.55175796" "Concs = 58.25965938"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     74.6926      -0.2339  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -52.088 -24.693  -7.788   6.970 152.201 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  74.6926    19.3363   3.863  0.00196 **
## Time[ind]    -0.2339     0.3818  -0.613  0.55064   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 47.78 on 13 degrees of freedom
## Multiple R-squared:  0.02807,    Adjusted R-squared:  -0.0467 
## F-statistic: 0.3754 on 1 and 13 DF,  p-value: 0.5506

## (Intercept)   Time[ind] 
##  74.6925954  -0.2339266 
##                 2.5 %     97.5 %
## (Intercept) 32.919023 116.466168
## Time[ind]   -1.058744   0.590891
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  45" "Indices =  46" "Indices =  47" "Indices =  48"
##  [5] "Indices =  49" "Indices =  50" "Indices =  51" "Indices =  52"
##  [9] "Indices =  53" "Indices =  54" "Indices =  55" "Indices =  56"
## [13] "Indices =  57" "Indices =  58"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 75"          "Concs = 75"          "Concs = 75"         
##  [4] "Concs = 35.05455395" "Concs = 40.30349338" "Concs = 44.1381674" 
##  [7] "Concs = 38.08049817" "Concs = 38.34527612" "Concs = 89.31881211"
## [10] "Concs = 40.27279664" "Concs = 55.95173867" "Concs = 37.82415225"
## [13] "Concs = 32.32010713" "Concs = 45.93427684"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     61.7586      -0.2706  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -22.64 -14.86  -2.33  12.54  35.68 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  61.7586     6.9259   8.917 1.22e-06 ***
## Time[ind]    -0.2706     0.1388  -1.950   0.0749 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.1 on 12 degrees of freedom
## Multiple R-squared:  0.2407, Adjusted R-squared:  0.1774 
## F-statistic: 3.803 on 1 and 12 DF,  p-value: 0.0749

## (Intercept)   Time[ind] 
##  61.7586076  -0.2706222 
##                  2.5 %      97.5 %
## (Intercept) 46.6682795 76.84893559
## Time[ind]   -0.5729691  0.03172479
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  59" "Indices =  60" "Indices =  61" "Indices =  62"
##  [5] "Indices =  63" "Indices =  64" "Indices =  65" "Indices =  66"
##  [9] "Indices =  67" "Indices =  68" "Indices =  69" "Indices =  70"
## [13] "Indices =  71" "Indices =  72" "Indices =  73"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 100"         "Concs = 100"         "Concs = 100"        
##  [4] "Concs = 65.75118371" "Concs = 61.03836189" "Concs = 86.42270417"
##  [7] "Concs = 18.77293974" "Concs = 84.04356305" "Concs = 89.30314297"
## [10] "Concs = 60.95565287" "Concs = 89.79580177" "Concs = 90.59062961"
## [13] "Concs = 56.03613412" "Concs = 94.58659729" "Concs = 89.70085579"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      82.175       -0.078  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -61.062 -15.897   9.468  16.185  19.431 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  82.1752     9.3919   8.750 8.28e-07 ***
## Time[ind]    -0.0780     0.1854  -0.421    0.681    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 23.21 on 13 degrees of freedom
## Multiple R-squared:  0.01343,    Adjusted R-squared:  -0.06246 
## F-statistic: 0.1769 on 1 and 13 DF,  p-value: 0.6809

## (Intercept)   Time[ind] 
## 82.17518132 -0.07800026 
##                  2.5 %      97.5 %
## (Intercept) 61.8852665 102.4650961
## Time[ind]   -0.4786239   0.3226233
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  74" "Indices =  75" "Indices =  76" "Indices =  77"
##  [5] "Indices =  78" "Indices =  79" "Indices =  80" "Indices =  81"
##  [9] "Indices =  82" "Indices =  83" "Indices =  84" "Indices =  85"
## [13] "Indices =  86" "Indices =  87" "Indices =  88"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 125"         "Concs = 125"         "Concs = 125"        
##  [4] "Concs = 62.24891641" "Concs = 54.68420677" "Concs = 91.10795719"
##  [7] "Concs = 51.66702524" "Concs = 65.6950903"  "Concs = 112.1237445"
## [10] "Concs = 62.81350539" "Concs = 74.14828799" "Concs = 93.87631612"
## [13] "Concs = 59.80299767" "Concs = 82.33654045" "Concs = 89.20514072"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     97.5253      -0.3217  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -38.016 -18.796  -1.593  22.439  27.475 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  97.5253    10.1778   9.582 2.95e-07 ***
## Time[ind]    -0.3217     0.2010  -1.601    0.133    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 25.15 on 13 degrees of freedom
## Multiple R-squared:  0.1646, Adjusted R-squared:  0.1004 
## F-statistic: 2.562 on 1 and 13 DF,  p-value: 0.1335

## (Intercept)   Time[ind] 
##   97.525349   -0.321659 
##                  2.5 %      97.5 %
## (Intercept) 75.5374944 119.5132038
## Time[ind]   -0.7558084   0.1124904
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  89"  "Indices =  90"  "Indices =  91"  "Indices =  92" 
##  [5] "Indices =  93"  "Indices =  94"  "Indices =  95"  "Indices =  96" 
##  [9] "Indices =  97"  "Indices =  98"  "Indices =  99"  "Indices =  100"
## [13] "Indices =  101" "Indices =  102" "Indices =  103"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 150"         "Concs = 150"         "Concs = 150"        
##  [4] "Concs = 37.15191594" "Concs = 76.95257401" "Concs = 82.83018255"
##  [7] "Concs = 89.28298886" "Concs = 103.9076465" "Concs = 88.89209516"
## [10] "Concs = 75.20034761" "Concs = 99.21349783" "Concs = 86.10641447"
## [13] "Concs = 85.35534061" "Concs = 86.89358929" "Concs = 19.45762438"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    115.9094      -0.6109  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -69.593 -16.302   6.326  25.199  34.091 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 115.9094    13.0063   8.912 6.73e-07 ***
## Time[ind]    -0.6109     0.2568  -2.379   0.0334 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 32.14 on 13 degrees of freedom
## Multiple R-squared:  0.3033, Adjusted R-squared:  0.2497 
## F-statistic: 5.659 on 1 and 13 DF,  p-value: 0.03337

## (Intercept)   Time[ind] 
## 115.9093503  -0.6109334 
##                 2.5 %       97.5 %
## (Intercept) 87.810974 144.00772609
## Time[ind]   -1.165735  -0.05613202
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  104" "Indices =  105" "Indices =  106" "Indices =  107"
##  [5] "Indices =  108" "Indices =  109" "Indices =  110" "Indices =  111"
##  [9] "Indices =  112" "Indices =  113" "Indices =  114" "Indices =  115"
## [13] "Indices =  116" "Indices =  117" "Indices =  118"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 200"         "Concs = 200"         "Concs = 200"        
##  [4] "Concs = 143.5820327" "Concs = 117.0381728" "Concs = 105.3992543"
##  [7] "Concs = 120.601107"  "Concs = 115.1379412" "Concs = 126.1830373"
## [10] "Concs = 91.91948648" "Concs = 106.6462813" "Concs = 72.50149496"
## [13] "Concs = 112.4063583" "Concs = 105.3992543" "Concs = 111.7531537"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    160.8018      -0.8264  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -43.006 -20.084  -4.823  25.656  39.198 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 160.8018    12.1956  13.185  6.7e-09 ***
## Time[ind]    -0.8264     0.2408  -3.432  0.00446 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 30.13 on 13 degrees of freedom
## Multiple R-squared:  0.4754, Adjusted R-squared:  0.435 
## F-statistic: 11.78 on 1 and 13 DF,  p-value: 0.00446

## (Intercept)   Time[ind] 
## 160.8018480  -0.8264276 
##                  2.5 %      97.5 %
## (Intercept) 134.454923 187.1487728
## Time[ind]    -1.346647  -0.3062086
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  119" "Indices =  120" "Indices =  121" "Indices =  122"
##  [5] "Indices =  123" "Indices =  124" "Indices =  125" "Indices =  126"
##  [9] "Indices =  127" "Indices =  128" "Indices =  129" "Indices =  130"
## [13] "Indices =  131" "Indices =  132" "Indices =  133"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 250"         "Concs = 250"         "Concs = 250"        
##  [4] "Concs = 105.2844752" "Concs = 83.9166222"  "Concs = 57.25407999"
##  [7] "Concs = 71.31021926" "Concs = 93.93871253" "Concs = 36.95777127"
## [10] "Concs = 77.4873567"  "Concs = 101.3134582" "Concs = 91.54349597"
## [13] "Concs = 58.38865626" "Concs = 74.14665992" "Concs = 61.1620649" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     164.214       -1.368  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -86.434 -45.128   9.433  26.595  85.786 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 164.2141    24.5533   6.688  1.5e-05 ***
## Time[ind]    -1.3684     0.4848  -2.823   0.0144 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 60.67 on 13 degrees of freedom
## Multiple R-squared:   0.38,  Adjusted R-squared:  0.3323 
## F-statistic: 7.967 on 1 and 13 DF,  p-value: 0.01439

## (Intercept)   Time[ind] 
##   164.21412    -1.36839 
##                  2.5 %      97.5 %
## (Intercept) 111.170007 217.2582237
## Time[ind]    -2.415744  -0.3210361
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  10 2.89 50 75 100 125 150 200 250
##  $ vel: num  -74.2 37.8 1169.6 1353.1 390 ...
##      sub        vel
## 1  10.00  -74.15048
## 2   2.89   37.75444
## 3  50.00 1169.63320
## 4  75.00 1353.11079
## 5 100.00  390.00131
## 6 125.00 1608.29494
## 7 150.00 3054.66698
## 8 200.00 4132.13800
## 9 250.00 6841.95007

fipsulf

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.226052779" "Concs = 0.249546426" "Concs = 0.249495111"
##  [7] "Concs = 0.556306401" "Concs = 0.629523416" "Concs = 0.545734442"
## [10] "Concs = 1.029532274" "Concs = 1.020828782" "Concs = 1.121529265"
## [13] "Concs = 1.478049545" "Concs = 1.552223152" "Concs = 1.605171177"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.01178      0.01724  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.08563 -0.02090 -0.01178  0.02194  0.10045 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.0117752  0.0194862   0.604    0.556    
## Time[ind]   0.0172434  0.0003848  44.817 1.23e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04815 on 13 degrees of freedom
## Multiple R-squared:  0.9936, Adjusted R-squared:  0.9931 
## F-statistic:  2009 on 1 and 13 DF,  p-value: 1.235e-15

## (Intercept)   Time[ind] 
##  0.01177521  0.01724336 
##                   2.5 %     97.5 %
## (Intercept) -0.03032210 0.05387251
## Time[ind]    0.01641215 0.01807457
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [7] "Concs = 0.072417652" "Concs = 0.105189206" "Concs = 0.093830232"
## [10] "Concs = 0.446059868" "Concs = 0.501873862" "Concs = 1.937676963"
## [13] "Concs = 0.541481009" "Concs = 0.713021528" "Concs = 0.948269563"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    -0.06729      0.01089  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.37110 -0.15983 -0.09602  0.05149  1.35172 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) -0.067286   0.164967  -0.408   0.6900   
## Time[ind]    0.010887   0.003257   3.342   0.0053 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4076 on 13 degrees of freedom
## Multiple R-squared:  0.4622, Adjusted R-squared:  0.4208 
## F-statistic: 11.17 on 1 and 13 DF,  p-value: 0.005297

## (Intercept)   Time[ind] 
## -0.06728624  0.01088737 
##                    2.5 %     97.5 %
## (Intercept) -0.423675199 0.28910272
## Time[ind]    0.003850487 0.01792426
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.509901494" "Concs = 0.497072024" "Concs = 0.573048602"
##  [7] "Concs = 0.208702278" "Concs = 1.224307072" "Concs = 0.86186791" 
## [10] "Concs = 2.640613398" "Concs = 2.278728642" "Concs = 1.938091721"
## [13] "Concs = 3.288556396" "Concs = 2.79424236"  "Concs = 2.85277407" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.21639      0.03149  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.9524 -0.2164 -0.1917  0.1181  1.8212 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.216386   0.251326   0.861    0.405    
## Time[ind]   0.031491   0.004962   6.346 2.55e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.621 on 13 degrees of freedom
## Multiple R-squared:  0.756,  Adjusted R-squared:  0.7372 
## F-statistic: 40.27 on 1 and 13 DF,  p-value: 2.552e-05

## (Intercept)   Time[ind] 
##   0.2163859   0.0314908 
##                   2.5 %     97.5 %
## (Intercept) -0.32657121 0.75934309
## Time[ind]    0.02077013 0.04221147
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.61596018"  "Concs = 0.004496637" "Concs = 0.393574273"
##  [7] "Concs = 1.00896852"  "Concs = 1.080335369" "Concs = 1.122428808"
## [10] "Concs = 0.794034486" "Concs = 1.567175192" "Concs = 1.445091993"
## [13] "Concs = 1.567376573" "Concs = 1.397216044"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.19848      0.01565  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.4288 -0.1985 -0.1010  0.3013  0.4543 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.19848    0.12829   1.547    0.148    
## Time[ind]    0.01565    0.00257   6.090 5.42e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3168 on 12 degrees of freedom
## Multiple R-squared:  0.7555, Adjusted R-squared:  0.7351 
## F-statistic: 37.08 on 1 and 12 DF,  p-value: 5.421e-05

## (Intercept)   Time[ind] 
##  0.19848307  0.01565313 
##                   2.5 %     97.5 %
## (Intercept) -0.08104254 0.47800868
## Time[ind]    0.01005261 0.02125366
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  60" "Indices =  61" "Indices =  62" "Indices =  63"
##  [5] "Indices =  64" "Indices =  65" "Indices =  66" "Indices =  67"
##  [9] "Indices =  68" "Indices =  69" "Indices =  70" "Indices =  71"
## [13] "Indices =  72" "Indices =  73" "Indices =  74"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 1.037370756" "Concs = 1.004548869" "Concs = 1.211451943"
##  [7] "Concs = 1.770038982" "Concs = 1.964421756" "Concs = 2.082784287"
## [10] "Concs = 2.421230649" "Concs = 2.716290502" "Concs = 2.511880669"
## [13] "Concs = 2.884476336" "Concs = 3.658963096" "Concs = 3.101044324"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.45746      0.03334  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.57339 -0.40714  0.05415  0.25624  0.62519 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.457459   0.159292   2.872   0.0131 *  
## Time[ind]   0.033338   0.003145  10.600 9.12e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3936 on 13 degrees of freedom
## Multiple R-squared:  0.8963, Adjusted R-squared:  0.8883 
## F-statistic: 112.4 on 1 and 13 DF,  p-value: 9.118e-08

## (Intercept)   Time[ind] 
##   0.4574592   0.0333378 
##                  2.5 %     97.5 %
## (Intercept) 0.11333032 0.80158804
## Time[ind]   0.02654299 0.04013261
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  75" "Indices =  76" "Indices =  77" "Indices =  78"
##  [5] "Indices =  79" "Indices =  80" "Indices =  81" "Indices =  82"
##  [9] "Indices =  83" "Indices =  84" "Indices =  85" "Indices =  86"
## [13] "Indices =  87" "Indices =  88" "Indices =  89"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 1.0685532"   "Concs = 1.193964217" "Concs = 1.061157254"
##  [7] "Concs = 1.739690158" "Concs = 1.568026457" "Concs = 1.831902381"
## [10] "Concs = 2.58185903"  "Concs = 2.518118409" "Concs = 2.706182414"
## [13] "Concs = 3.388713261" "Concs = 3.265199632" "Concs = 3.360717697"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.38590      0.03504  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.38590 -0.22611  0.09385  0.18765  0.39495 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.385901   0.113655   3.395  0.00478 ** 
## Time[ind]   0.035035   0.002244  15.612 8.42e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2808 on 13 degrees of freedom
## Multiple R-squared:  0.9494, Adjusted R-squared:  0.9455 
## F-statistic: 243.7 on 1 and 13 DF,  p-value: 8.42e-10

## (Intercept)   Time[ind] 
##  0.38590066  0.03503517 
##                  2.5 %     97.5 %
## (Intercept) 0.14036476 0.63143656
## Time[ind]   0.03018707 0.03988327
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  90"  "Indices =  91"  "Indices =  92"  "Indices =  93" 
##  [5] "Indices =  94"  "Indices =  95"  "Indices =  96"  "Indices =  97" 
##  [9] "Indices =  98"  "Indices =  99"  "Indices =  100" "Indices =  101"
## [13] "Indices =  102" "Indices =  103" "Indices =  104"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 1.513101462" "Concs = 1.254618226" "Concs = 1.316915121"
##  [7] "Concs = 1.847166036" "Concs = 2.06265471"  "Concs = 2.225655093"
## [10] "Concs = 3.029089226" "Concs = 2.818619179" "Concs = 2.892261352"
## [13] "Concs = 3.395108251" "Concs = 3.493680617" "Concs = 3.346621743"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.57092      0.03527  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.5709 -0.3742  0.1547  0.2802  0.5967 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.570919   0.171417   3.331  0.00542 ** 
## Time[ind]   0.035268   0.003385  10.420 1.11e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4236 on 13 degrees of freedom
## Multiple R-squared:  0.8931, Adjusted R-squared:  0.8848 
## F-statistic: 108.6 on 1 and 13 DF,  p-value: 1.114e-07

## (Intercept)   Time[ind] 
##  0.57091928  0.03526787 
##                  2.5 %     97.5 %
## (Intercept) 0.20059443 0.94124413
## Time[ind]   0.02795582 0.04257992
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  105" "Indices =  106" "Indices =  107" "Indices =  108"
##  [5] "Indices =  109" "Indices =  110" "Indices =  111" "Indices =  112"
##  [9] "Indices =  113" "Indices =  114" "Indices =  115" "Indices =  116"
## [13] "Indices =  117" "Indices =  118" "Indices =  119"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.921840151" "Concs = 1.265455207" "Concs = 0.083794693"
##  [7] "Concs = 1.758009212" "Concs = 1.131761977" "Concs = 2.14032494" 
## [10] "Concs = 3.119569212" "Concs = 5.219960219" "Concs = 3.68483357" 
## [13] "Concs = 4.382618411" "Concs = 4.121095689" "Concs = 4.42249183" 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     0.12797      0.05185  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.8219 -0.3919 -0.1280  0.2171  1.9810 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.12797    0.28111   0.455    0.656    
## Time[ind]    0.05185    0.00555   9.342 3.94e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6946 on 13 degrees of freedom
## Multiple R-squared:  0.8703, Adjusted R-squared:  0.8604 
## F-statistic: 87.26 on 1 and 13 DF,  p-value: 3.942e-07

## (Intercept)   Time[ind] 
##  0.12796676  0.05185001 
##                   2.5 %     97.5 %
## (Intercept) -0.47932924 0.73526276
## Time[ind]    0.03985897 0.06384104
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  120" "Indices =  121" "Indices =  122" "Indices =  123"
##  [5] "Indices =  124" "Indices =  125" "Indices =  126" "Indices =  127"
##  [9] "Indices =  128" "Indices =  129" "Indices =  130" "Indices =  131"
## [13] "Indices =  132" "Indices =  133" "Indices =  134"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.688691412" "Concs = 0.680203691" "Concs = 0.671715969"
##  [7] "Concs = 1.128032043" "Concs = 1.057705208" "Concs = 1.0791266"  
## [10] "Concs = 1.670842039" "Concs = 1.655483305" "Concs = 1.672054571"
## [13] "Concs = 2.11584115"  "Concs = 2.394723427" "Concs = 2.276703681"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      0.2111       0.0238  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.23753 -0.14388  0.03278  0.11632  0.20285 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.211083   0.063521   3.323   0.0055 ** 
## Time[ind]   0.023803   0.001254  18.978 7.35e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.157 on 13 degrees of freedom
## Multiple R-squared:  0.9652, Adjusted R-squared:  0.9625 
## F-statistic: 360.2 on 1 and 13 DF,  p-value: 7.353e-11

## (Intercept)   Time[ind] 
##  0.21108314  0.02380321 
##                  2.5 %     97.5 %
## (Intercept) 0.07385384 0.34831244
## Time[ind]   0.02109362 0.02651279
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  10 2.89 50 75 100 125 150 200 250
##  $ vel: num  86.2 54.4 157.5 78.3 166.7 ...
##      sub       vel
## 1  10.00  86.21679
## 2   2.89  54.43687
## 3  50.00 157.45399
## 4  75.00  78.26567
## 5 100.00 166.68901
## 6 125.00 175.17585
## 7 150.00 176.33933
## 8 200.00 259.25003
## 9 250.00 119.01603

exposure experiment analysis

Results presentation and discussion for parent analytes (atrazine, triadimenon, and fipronil) and their xenobiotic metabolites.

Toxicity of parents and metabolites discussion.

Microsomal analysis of soil and amphibian data for 0 (soil only), 2, 4, 12, 24, and 48 hours after exposure.

Database has factors for time, parent (mapped to analyte), analyte (can be either parent or metabolite), matrix (amphibian or soil), and tank (potentially a nuisance variable).

## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame':  352 obs. of  6 variables:
##  $ time     : int  2 2 2 2 4 4 4 4 12 12 ...
##  $ parent   : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte  : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix   : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 1 1 1 1 1 ...
##  $ conc     : num  3.07 3.69 4.7 1.89 7.62 ...
##  $ replicate: Factor w/ 4 levels "1","2","3","4": 1 2 3 4 1 2 3 4 1 2 ...
##  - attr(*, "vars")=List of 4
##   ..$ : symbol parent
##   ..$ : symbol analyte
##   ..$ : symbol matrix
##   ..$ : symbol time
##  - attr(*, "drop")= logi TRUE
##  - attr(*, "indices")=List of 86
##   ..$ : int  0 1 2 3
##   ..$ : int  4 5 6 7
##   ..$ : int  8 9 10 11
##   ..$ : int  12 13 14 15
##   ..$ : int  16 17 18 19
##   ..$ : int  20 21 22 23
##   ..$ : int  24 25 26 27
##   ..$ : int  28 29 30 31
##   ..$ : int  32 33 34 35
##   ..$ : int  36 37 38 39
##   ..$ : int  40 41 42 43
##   ..$ : int  88 89 90 91
##   ..$ : int  92 93 94 95
##   ..$ : int  96 97 98 99
##   ..$ : int  100 101 102 103
##   ..$ : int  104 105 106 107
##   ..$ : int  108 109 110 111
##   ..$ : int  112 113 114 115
##   ..$ : int  116 117 118 119
##   ..$ : int  120 121 122 123
##   ..$ : int  124 125 126 127
##   ..$ : int  128 129 130 131
##   ..$ : int  44 45 46 47
##   ..$ : int  48 49 50 51
##   ..$ : int  52 53 54 55
##   ..$ : int  56 57 58 59
##   ..$ : int  60 61 62 63
##   ..$ : int  64 65 66 67
##   ..$ : int  68 69 70 71
##   ..$ : int  72 73 74 75
##   ..$ : int  76 77 78 79
##   ..$ : int  80 81 82 83
##   ..$ : int  84 85 86 87
##   ..$ : int  264 265 266 267
##   ..$ : int  268 269 270 271
##   ..$ : int  272 273 274 275
##   ..$ : int  276 277 278 279
##   ..$ : int  280 281 282 283
##   ..$ : int  284 285 286 287 288 289 290 291
##   ..$ : int  292 293 294 295
##   ..$ : int  296 297 298 299
##   ..$ : int  300 301 302 303
##   ..$ : int  304 305 306 307
##   ..$ : int  308 309 310 311
##   ..$ : int  312 313 314 315
##   ..$ : int  316 317 318 319
##   ..$ : int  320 321 322 323
##   ..$ : int  324 325 326 327
##   ..$ : int  328 329 330 331 332 333 334 335
##   ..$ : int  336 337 338 339
##   ..$ : int  340 341 342 343
##   ..$ : int  344 345 346 347
##   ..$ : int  348 349 350 351
##   ..$ : int  176 177 178 179
##   ..$ : int  180 181 182 183
##   ..$ : int  184 185 186 187
##   ..$ : int  188 189 190 191
##   ..$ : int  192 193 194 195
##   ..$ : int  196 197 198 199
##   ..$ : int  200 201 202 203
##   ..$ : int  204 205 206 207
##   ..$ : int  208 209 210 211
##   ..$ : int  212 213 214 215
##   ..$ : int  216 217 218 219
##   ..$ : int  220 221 222 223
##   ..$ : int  224 225 226 227
##   ..$ : int  228 229 230 231
##   ..$ : int  232 233 234 235
##   ..$ : int  236 237 238 239
##   ..$ : int  240 241 242 243
##   ..$ : int  244 245 246 247
##   ..$ : int  248 249 250 251
##   ..$ : int  252 253 254 255
##   ..$ : int  256 257 258 259
##   ..$ : int  260 261 262 263
##   ..$ : int  132 133 134 135
##   ..$ : int  136 137 138 139
##   ..$ : int  140 141 142 143
##   ..$ : int  144 145 146 147
##   ..$ : int  148 149 150 151
##   ..$ : int  152 153 154 155
##   ..$ : int  156 157 158 159
##   ..$ : int  160 161 162 163
##   ..$ : int  164 165 166 167
##   ..$ : int  168 169 170 171
##   ..$ : int  172 173 174 175
##  - attr(*, "group_sizes")= int  4 4 4 4 4 4 4 4 4 4 ...
##  - attr(*, "biggest_group_size")= int 8
##  - attr(*, "labels")='data.frame':   86 obs. of  4 variables:
##   ..$ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ analyte: Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 2 2 2 2 2 ...
##   ..$ time   : int  2 4 12 24 48 0 2 4 12 24 ...
##   ..- attr(*, "vars")=List of 4
##   .. ..$ : symbol parent
##   .. ..$ : symbol analyte
##   .. ..$ : symbol matrix
##   .. ..$ : symbol time
##   ..- attr(*, "drop")= logi TRUE
## Source: local data frame [352 x 6]
## Groups: parent, analyte, matrix, time [86]
## 
##     time   parent  analyte matrix     conc replicate
##    (int)   (fctr)   (fctr) (fctr)    (dbl)    (fctr)
## 1      2 atrazine atrazine amphib 3.068203         1
## 2      2 atrazine atrazine amphib 3.689640         2
## 3      2 atrazine atrazine amphib 4.701166         3
## 4      2 atrazine atrazine amphib 1.892494         4
## 5      4 atrazine atrazine amphib 7.624610         1
## 6      4 atrazine atrazine amphib 4.134300         2
## 7      4 atrazine atrazine amphib 2.050779         3
## 8      4 atrazine atrazine amphib 7.626486         4
## 9     12 atrazine atrazine amphib 2.452278         1
## 10    12 atrazine atrazine amphib 3.786893         2
## ..   ...      ...      ...    ...      ...       ...
## Source: local data frame [86 x 7]
## Groups: parent, analyte, matrix [?]
## 
##      parent  analyte matrix  time count  ConcMean    ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)     (dbl)     (dbl)
## 1  atrazine atrazine amphib     2     4  3.337876 1.1753225
## 2  atrazine atrazine amphib     4     4  5.359044 2.7518903
## 3  atrazine atrazine amphib    12     4  3.123811 1.2566289
## 4  atrazine atrazine amphib    24     4  1.554919 0.6096102
## 5  atrazine atrazine amphib    48     4  1.001887 0.3545473
## 6  atrazine atrazine   soil     0     4 15.930920 2.5911041
## 7  atrazine atrazine   soil     2     4 19.029034 4.3534303
## 8  atrazine atrazine   soil     4     4 18.770091 2.6953158
## 9  atrazine atrazine   soil    12     4 20.614190 3.8918511
## 10 atrazine atrazine   soil    24     4 24.996196 4.4473828
## ..      ...      ...    ...   ...   ...       ...       ...
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Thu Feb  4 23:18:14 2016 -->
## <table border=1>
## <tr> <th>  </th> <th> parent </th> <th> analyte </th> <th> matrix </th> <th> time </th> <th> count </th> <th> ConcMean </th> <th> ConcSD </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 3.34 </td> <td align="right"> 1.18 </td> </tr>
##   <tr> <td align="right"> 2 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 5.36 </td> <td align="right"> 2.75 </td> </tr>
##   <tr> <td align="right"> 3 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 3.12 </td> <td align="right"> 1.26 </td> </tr>
##   <tr> <td align="right"> 4 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 1.55 </td> <td align="right"> 0.61 </td> </tr>
##   <tr> <td align="right"> 5 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 1.00 </td> <td align="right"> 0.35 </td> </tr>
##   <tr> <td align="right"> 6 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 15.93 </td> <td align="right"> 2.59 </td> </tr>
##   <tr> <td align="right"> 7 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 19.03 </td> <td align="right"> 4.35 </td> </tr>
##   <tr> <td align="right"> 8 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 18.77 </td> <td align="right"> 2.70 </td> </tr>
##   <tr> <td align="right"> 9 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 20.61 </td> <td align="right"> 3.89 </td> </tr>
##   <tr> <td align="right"> 10 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 25.00 </td> <td align="right"> 4.45 </td> </tr>
##   <tr> <td align="right"> 11 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 26.43 </td> <td align="right"> 4.38 </td> </tr>
##   <tr> <td align="right"> 12 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 13 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.03 </td> </tr>
##   <tr> <td align="right"> 14 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.05 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 15 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 16 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 17 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 18 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 19 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 20 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 21 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 22 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 23 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.33 </td> <td align="right"> 0.12 </td> </tr>
##   <tr> <td align="right"> 24 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.94 </td> <td align="right"> 0.76 </td> </tr>
##   <tr> <td align="right"> 25 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 1.08 </td> <td align="right"> 0.51 </td> </tr>
##   <tr> <td align="right"> 26 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 1.99 </td> <td align="right"> 1.35 </td> </tr>
##   <tr> <td align="right"> 27 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.66 </td> <td align="right"> 0.53 </td> </tr>
##   <tr> <td align="right"> 28 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 29 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> -0.01 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 30 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 31 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.07 </td> </tr>
##   <tr> <td align="right"> 32 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.03 </td> </tr>
##   <tr> <td align="right"> 33 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.06 </td> <td align="right"> 0.06 </td> </tr>
##   <tr> <td align="right"> 34 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 1.87 </td> <td align="right"> 1.35 </td> </tr>
##   <tr> <td align="right"> 35 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 1.30 </td> <td align="right"> 0.52 </td> </tr>
##   <tr> <td align="right"> 36 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.57 </td> <td align="right"> 0.24 </td> </tr>
##   <tr> <td align="right"> 37 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.27 </td> <td align="right"> 0.05 </td> </tr>
##   <tr> <td align="right"> 38 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.21 </td> <td align="right"> 0.13 </td> </tr>
##   <tr> <td align="right"> 39 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   8 </td> <td align="right"> 0.41 </td> <td align="right"> 0.45 </td> </tr>
##   <tr> <td align="right"> 40 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.87 </td> <td align="right"> 0.24 </td> </tr>
##   <tr> <td align="right"> 41 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.82 </td> <td align="right"> 0.17 </td> </tr>
##   <tr> <td align="right"> 42 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.70 </td> <td align="right"> 0.11 </td> </tr>
##   <tr> <td align="right"> 43 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.36 </td> <td align="right"> 0.06 </td> </tr>
##   <tr> <td align="right"> 44 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.35 </td> <td align="right"> 0.29 </td> </tr>
##   <tr> <td align="right"> 45 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.40 </td> <td align="right"> 0.48 </td> </tr>
##   <tr> <td align="right"> 46 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.61 </td> <td align="right"> 0.57 </td> </tr>
##   <tr> <td align="right"> 47 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 1.25 </td> <td align="right"> 0.53 </td> </tr>
##   <tr> <td align="right"> 48 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.91 </td> <td align="right"> 0.57 </td> </tr>
##   <tr> <td align="right"> 49 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   8 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 50 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 51 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 52 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 53 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 54 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.06 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 55 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.05 </td> </tr>
##   <tr> <td align="right"> 56 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 57 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 58 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 59 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 60 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 61 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 62 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 63 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 64 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 65 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 66 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.13 </td> <td align="right"> 0.05 </td> </tr>
##   <tr> <td align="right"> 67 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.05 </td> </tr>
##   <tr> <td align="right"> 68 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 69 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.03 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 70 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 71 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 72 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 73 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 74 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 75 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 76 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.39 </td> <td align="right"> 0.08 </td> </tr>
##   <tr> <td align="right"> 77 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.55 </td> <td align="right"> 0.30 </td> </tr>
##   <tr> <td align="right"> 78 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.75 </td> <td align="right"> 0.32 </td> </tr>
##   <tr> <td align="right"> 79 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.87 </td> <td align="right"> 0.86 </td> </tr>
##   <tr> <td align="right"> 80 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.25 </td> <td align="right"> 0.08 </td> </tr>
##   <tr> <td align="right"> 81 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 3.11 </td> <td align="right"> 0.85 </td> </tr>
##   <tr> <td align="right"> 82 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 3.66 </td> <td align="right"> 1.34 </td> </tr>
##   <tr> <td align="right"> 83 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 5.28 </td> <td align="right"> 0.37 </td> </tr>
##   <tr> <td align="right"> 84 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 5.93 </td> <td align="right"> 1.00 </td> </tr>
##   <tr> <td align="right"> 85 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 4.82 </td> <td align="right"> 0.32 </td> </tr>
##   <tr> <td align="right"> 86 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 4.18 </td> <td align="right"> 0.44 </td> </tr>
##    </table>

The amphibian data set summary statistics. Atrazine peaks at 4 hours and then declines monotonically. DEA peaks at 12 hours and DIA at 24. Fipronil steadily declines from its first observation at 2 hours with fipronil sulfone not peaking until 24 hours. Triadimenon peaks at 24 hours with its metabolites tdla and tdlb peaking at 4 hours.

## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame':  86 obs. of  7 variables:
##  $ parent  : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix  : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 2 2 2 2 2 ...
##  $ time    : int  2 4 12 24 48 0 2 4 12 24 ...
##  $ count   : int  4 4 4 4 4 4 4 4 4 4 ...
##  $ ConcMean: num  3.34 5.36 3.12 1.55 1 ...
##  $ ConcSD  : num  1.175 2.752 1.257 0.61 0.355 ...
##  - attr(*, "vars")=List of 3
##   ..$ : symbol parent
##   ..$ : symbol analyte
##   ..$ : symbol matrix
##  - attr(*, "drop")= logi TRUE
## Source: local data frame [6 x 7]
## Groups: parent, analyte, matrix [2]
## 
##     parent  analyte matrix  time count   ConcMean     ConcSD
##     (fctr)   (fctr) (fctr) (int) (int)      (dbl)      (dbl)
## 1 atrazine atrazine amphib     2     4 3.33787563 1.17532253
## 2 atrazine atrazine amphib     4     4 5.35904387 2.75189034
## 3 atrazine atrazine amphib    12     4 3.12381130 1.25662887
## 4 atrazine atrazine amphib    24     4 1.55491895 0.60961016
## 5 atrazine atrazine amphib    48     4 1.00188749 0.35454734
## 6 atrazine      dea amphib     2     4 0.01389877 0.00522407
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
## 
##      parent  analyte matrix  time count   ConcMean     ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)      (dbl)      (dbl)
## 1  atrazine atrazine amphib     2     4 3.33787563 1.17532253
## 2  atrazine atrazine amphib     4     4 5.35904387 2.75189034
## 3  atrazine atrazine amphib    12     4 3.12381130 1.25662887
## 4  atrazine atrazine amphib    24     4 1.55491895 0.60961016
## 5  atrazine atrazine amphib    48     4 1.00188749 0.35454734
## 6  atrazine      dea amphib     2     4 0.01389877 0.00522407
## 7  atrazine      dea amphib     4     4 0.04436711 0.02843181
## 8  atrazine      dea amphib    12     4 0.05402182 0.01282235
## 9  atrazine      dea amphib    24     4 0.03652473 0.01310278
## 10 atrazine      dea amphib    48     4 0.01951501 0.01958540
## 11 atrazine      dia amphib     2     4 0.32878185 0.12495746
## 12 atrazine      dia amphib     4     4 0.94192818 0.76074427
## 13 atrazine      dia amphib    12     4 1.08350960 0.50576827
## 14 atrazine      dia amphib    24     4 1.98835970 1.34925248
## 15 atrazine      dia amphib    48     4 0.66238821 0.53051448
## [1] "atrazine"
## [1] "dea"
## [1] "dia"
## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
## 
##      parent  analyte matrix  time count  ConcMean     ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)     (dbl)      (dbl)
## 1  fipronil fipronil amphib     2     4 1.8670398 1.34631230
## 2  fipronil fipronil amphib     4     4 1.3005836 0.52188454
## 3  fipronil fipronil amphib    12     4 0.5659565 0.24026633
## 4  fipronil fipronil amphib    24     4 0.2676732 0.05106111
## 5  fipronil fipronil amphib    48     4 0.2119504 0.13140536
## 6  fipronil  fipsulf amphib     2     4 0.3465734 0.28711156
## 7  fipronil  fipsulf amphib     4     4 0.3966089 0.47739157
## 8  fipronil  fipsulf amphib    12     4 0.6129114 0.57346517
## 9  fipronil  fipsulf amphib    24     4 1.2528179 0.52648677
## 10 fipronil  fipsulf amphib    48     4 0.9067126 0.56596417
## Source: local data frame [0 x 7]
## Groups: parent, analyte, matrix [0]
## 
## Variables not shown: parent (fctr), analyte (fctr), matrix (fctr), time
##   (int), count (int), ConcMean (dbl), ConcSD (dbl)

The soil data set summary statistics. Atrazine in soil showing an upwards trend (need to test if significant) with dia and dea levels very low indicating little degradation in soil over the 48 hour period. Fipronil and triadimenon data also indicating little degradation in soil.

## Source: local data frame [18 x 7]
## Groups: parent, analyte, matrix [3]
## 
##      parent  analyte matrix  time count     ConcMean      ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)        (dbl)       (dbl)
## 1  atrazine atrazine   soil     0     4 15.930919692 2.591104068
## 2  atrazine atrazine   soil     2     4 19.029034412 4.353430337
## 3  atrazine atrazine   soil     4     4 18.770091080 2.695315758
## 4  atrazine atrazine   soil    12     4 20.614190363 3.891851074
## 5  atrazine atrazine   soil    24     4 24.996195532 4.447382801
## 6  atrazine atrazine   soil    48     4 26.434744900 4.377099498
## 7  atrazine      dea   soil     0     4  0.000000000 0.000000000
## 8  atrazine      dea   soil     2     4  0.001570429 0.000633009
## 9  atrazine      dea   soil     4     4  0.002999216 0.001537652
## 10 atrazine      dea   soil    12     4  0.005469015 0.004234880
## 11 atrazine      dea   soil    24     4  0.007308439 0.001736211
## 12 atrazine      dea   soil    48     4  0.008784632 0.003772339
## 13 atrazine      dia   soil     0     4  0.000000000 0.000000000
## 14 atrazine      dia   soil     2     4 -0.007727286 0.007374085
## 15 atrazine      dia   soil     4     4  0.020538600 0.020166308
## 16 atrazine      dia   soil    12     4  0.077036921 0.067772652
## 17 atrazine      dia   soil    24     4  0.042975804 0.030007793
## 18 atrazine      dia   soil    48     4  0.063693292 0.058241606
## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
## 
##      parent  analyte matrix  time count   ConcMean      ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)      (dbl)       (dbl)
## 1  fipronil fipronil   soil     2     8 0.40768123 0.447265792
## 2  fipronil fipronil   soil     4     4 0.86826316 0.244191727
## 3  fipronil fipronil   soil    12     4 0.81738069 0.169691335
## 4  fipronil fipronil   soil    24     4 0.70225877 0.108745058
## 5  fipronil fipronil   soil    48     4 0.35560948 0.058543752
## 6  fipronil  fipsulf   soil     2     8 0.01022479 0.012898421
## 7  fipronil  fipsulf   soil     4     4 0.02193831 0.010765665
## 8  fipronil  fipsulf   soil    12     4 0.01829893 0.005013814
## 9  fipronil  fipsulf   soil    24     4 0.01917848 0.009139211
## 10 fipronil  fipsulf   soil    48     4 0.01262887 0.005517408
## Source: local data frame [0 x 7]
## Groups: parent, analyte, matrix [0]
## 
## Variables not shown: parent (fctr), analyte (fctr), matrix (fctr), time
##   (int), count (int), ConcMean (dbl), ConcSD (dbl)
pdf(paste(micro.graphics,"data_mean_scatterplot",".pdf", sep=""))
  par(mfrow=c(3,1))
  print(parents)
## [1] atrazine    triadimefon fipronil   
## Levels: atrazine fipronil triadimefon
  for(parent in parents){
    i=0
    print(parent)
    temp.parent <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
    print(temp.parent)
    parent.analytes <- unique(temp.parent$analyte)
    for(analyte in parent.analytes){
      print(parent)
      print(analyte) 
      analytetemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$analyte==analyte),]
      xvalues <- as.numeric(as.character(analytetemp$time))
      points.y <- micro.amphib[which(micro.amphib$analyte==analyte),]$conc
      points.x <- as.numeric(as.character(micro.amphib[which(micro.amphib$analyte==analyte),]$time))
      #create empty plot if needed
      if(i==0){
        parenttemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
        maxconc <- max(points.y) 
        plot(xvalues,analytetemp$ConcMean,type="l", xlim=c(0,48),
             ylim = c(0,maxconc), main=parent,col="black", xlab="Hours", ylab="Concentration")
        axis(1,at=xvalues)
        i=1
      }
      #add line for parent metabolite
      if(analyte %in% parents){
        lines(xvalues,analytetemp$ConcMean,type="l",col="red")
        points(points.x, points.y, col = "red")
      }else{
      #add line for daughter metabolite
        lines(xvalues,analytetemp$ConcMean,type="l",col="blue")
        points(points.x, points.y, col = "blue")
      }
    }
  }
## [1] "atrazine"
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
## 
##      parent  analyte matrix  time count   ConcMean     ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)      (dbl)      (dbl)
## 1  atrazine atrazine amphib     2     4 3.33787563 1.17532253
## 2  atrazine atrazine amphib     4     4 5.35904387 2.75189034
## 3  atrazine atrazine amphib    12     4 3.12381130 1.25662887
## 4  atrazine atrazine amphib    24     4 1.55491895 0.60961016
## 5  atrazine atrazine amphib    48     4 1.00188749 0.35454734
## 6  atrazine      dea amphib     2     4 0.01389877 0.00522407
## 7  atrazine      dea amphib     4     4 0.04436711 0.02843181
## 8  atrazine      dea amphib    12     4 0.05402182 0.01282235
## 9  atrazine      dea amphib    24     4 0.03652473 0.01310278
## 10 atrazine      dea amphib    48     4 0.01951501 0.01958540
## 11 atrazine      dia amphib     2     4 0.32878185 0.12495746
## 12 atrazine      dia amphib     4     4 0.94192818 0.76074427
## 13 atrazine      dia amphib    12     4 1.08350960 0.50576827
## 14 atrazine      dia amphib    24     4 1.98835970 1.34925248
## 15 atrazine      dia amphib    48     4 0.66238821 0.53051448
## [1] "atrazine"
## [1] "atrazine"
## [1] "atrazine"
## [1] "dea"
## [1] "atrazine"
## [1] "dia"
## [1] "triadimefon"
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
## 
##         parent     analyte matrix  time count   ConcMean      ConcSD
##         (fctr)      (fctr) (fctr) (int) (int)      (dbl)       (dbl)
## 1  triadimefon        tdla amphib     2     4 0.05514470 0.021089764
## 2  triadimefon        tdla amphib     4     4 0.08150175 0.046221502
## 3  triadimefon        tdla amphib    12     4 0.03632384 0.015222899
## 4  triadimefon        tdla amphib    24     4 0.02400790 0.007522554
## 5  triadimefon        tdla amphib    48     4 0.01549908 0.004845715
## 6  triadimefon        tdlb amphib     2     4 0.08362714 0.016364595
## 7  triadimefon        tdlb amphib     4     4 0.13009543 0.054315693
## 8  triadimefon        tdlb amphib    12     4 0.07664673 0.048553355
## 9  triadimefon        tdlb amphib    24     4 0.04183235 0.011652266
## 10 triadimefon        tdlb amphib    48     4 0.02950214 0.003438978
## 11 triadimefon triadimefon amphib     2     4 0.38678831 0.075852995
## 12 triadimefon triadimefon amphib     4     4 0.54862458 0.300394386
## 13 triadimefon triadimefon amphib    12     4 0.75491439 0.318237965
## 14 triadimefon triadimefon amphib    24     4 0.86540039 0.860421208
## 15 triadimefon triadimefon amphib    48     4 0.24868748 0.079848623
## [1] "triadimefon"
## [1] "tdla"
## [1] "triadimefon"
## [1] "tdlb"
## [1] "triadimefon"
## [1] "triadimefon"
## [1] "fipronil"
## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
## 
##      parent  analyte matrix  time count  ConcMean     ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)     (dbl)      (dbl)
## 1  fipronil fipronil amphib     2     4 1.8670398 1.34631230
## 2  fipronil fipronil amphib     4     4 1.3005836 0.52188454
## 3  fipronil fipronil amphib    12     4 0.5659565 0.24026633
## 4  fipronil fipronil amphib    24     4 0.2676732 0.05106111
## 5  fipronil fipronil amphib    48     4 0.2119504 0.13140536
## 6  fipronil  fipsulf amphib     2     4 0.3465734 0.28711156
## 7  fipronil  fipsulf amphib     4     4 0.3966089 0.47739157
## 8  fipronil  fipsulf amphib    12     4 0.6129114 0.57346517
## 9  fipronil  fipsulf amphib    24     4 1.2528179 0.52648677
## 10 fipronil  fipsulf amphib    48     4 0.9067126 0.56596417
## [1] "fipronil"
## [1] "fipronil"
## [1] "fipronil"
## [1] "fipsulf"
dev.off()
## quartz_off_screen 
##                 2

la de da

turn times series to zoo objects

estimate lambdas using maximum likelihood for each time series

library(maxLik)

MLexp <- function(times, data){

expLik <- function(param) { y <- data t <- times alpha1 <- param[1] lambda1 <- param[2]-1(alpha1-lambda1t) - y/(exp(alpha1-lambda1*t)) }

max.fit <- maxLik(expLik, start = c(1,1)) crit <- qt(.975, length(data)-2) max.intercept.CI <- c(summary(max.fit)\(est[1,1]-crit*summary(max.fit)\)est[1,2],summary(max.fit)\(est[1,1]+crit*summary(max.fit)\)est[1,2]) max.decayrate.CI <- c(-1summary(max.fit)\(est[2,1]-crit*summary(max.fit)\)est[2,2],-1summary(max.fit)\(est[2,1]+crit*summary(max.fit)\)est[2,2]) max.halflife.CI <- c(log(2)/max.decayrate.CI[2],log(2)/max.decayrate.CI[1])

paste(“MLE for Initial Concentration =”,max.fit\(est[1], "MLE for decay rate =", max.fit\)est[2], “MLE for half life =”, -log(.5)/max.fit$est[2])

temp.list <- list(max.fit\(est[1], max.fit\)est[2], -log(.5)/max.fit$est[2], max.intercept.CI, max.decayrate.CI, max.halflife.CI, vcov(max.fit) ) return(temp.list) }

MLexp.intercept <- function(times, data) { temp.fit <- MLexp(times,data) temp.fit[[1]] }

MLexp.decayrate <- function(times, data) { temp.fit <- MLexp(times,data) temp.fit[[2]] }

MLexp.halflife <- function(times,data) { temp.fit <- MLexp(times,data) temp.fit[[3]] }

MLexp.intercept.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[4]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }

MLexp.decayrate.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[5]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }

MLexp.halflife.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[6]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }

microsome experiment analysis

data in csv format

>>>>>>> 9263dffc0a4ecd1a3c01530af7902f610f813b3a